full_model_6DOF.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modelo Dinámico del submarino: 6-DOF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy.physics.mechanics import ReferenceFrame,Point,dynamicsymbols\n",
    "from sympy.physics.mechanics import Point,RigidBody,inertia, KanesMethod\n",
    "from sympy import latex,pprint,symbols,init_printing\n",
    "from sympy.algebras.quaternion import Quaternion\n",
    "from sympy.physics.mechanics import LagrangesMethod, Lagrangian\n",
    "from scipy.integrate import odeint\n",
    "from sympy import lambdify\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation\n",
    "import numpy as np\n",
    "import sys \n",
    "import sympy\n",
    "sys.path.append(\"../tools\")\n",
    "from vis import Visualizer\n",
    "%matplotlib inline\n",
    "init_printing() # Para visualizar símbolos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getComponents(expr,frame,simplify=True):\n",
    "    if simplify:\n",
    "        return [expr.dot(frame.x).simplify(),expr.dot(frame.y).simplify(),expr.dot(frame.z).simplify()]\n",
    "    else:\n",
    "        return [expr.dot(frame.x),expr.dot(frame.y),expr.dot(frame.z)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "t=symbols('t')\n",
    "#Parametros inerciales del modelo\n",
    "[m,Ixx,Iyy,Izz,g]=symbols('m,Ixx,Iyy,Izz,g')\n",
    "#Parametros geometricos del modelo\n",
    "[x1,y1,x2,y2,x3,y3,x4,y4,x5,y5,x6,y6,beta1,beta2,beta3,beta4]=symbols('x1,y1,x2,y2,x3,y3,x4,y4,x5,y5,x6,y6,beta1,beta2,beta3,beta4')\n",
    "#Parametros dinámicos del modelo\n",
    "[q1,q2,q3,q4,q5,q6]=dynamicsymbols('q1 q2 q3 q4 q5 q6')\n",
    "q1d,q2d,q3d,q4d,q5d,q6d=dynamicsymbols('q1 q2 q3 q4 q5 q6',1)\n",
    "q1dd,q2dd,q3dd,q4dd,q5dd,q6dd=dynamicsymbols('q1 q2 q3 q4 q5 q6',2)\n",
    "\n",
    "#Definir marcos de referencia de importancia\n",
    "N=ReferenceFrame('N')\n",
    "A1=N.orientnew('A1','Axis',(q4,N.z))\n",
    "A2=A1.orientnew('A2','Axis',(q5,A1.y))\n",
    "A=A2.orientnew('A','Axis',(q6,A2.x))\n",
    "B1=A.orientnew('B1','Axis',(-beta1,A.z))\n",
    "B2=A.orientnew('B2','Axis',(beta2,A.z))\n",
    "B3=A.orientnew('B3','Axis',(-beta3,A.z))\n",
    "B4=A.orientnew('B4','Axis',(beta4,A.z))\n",
    "B5=A.orientnew('B6','Axis',(np.deg2rad(90),A.x))\n",
    "B6=A.orientnew('B6','Axis',(np.deg2rad(90),A.x))\n",
    "\n",
    "#Definir puntos de interes\n",
    "O=Point('O')\n",
    "a=O.locatenew('A',q1*N.x+q2*N.y+q3*N.z)\n",
    "A.set_ang_vel(A,q4d*N.z+q5d*A1.y+q6d*A2.x)\n",
    "a.set_vel(N,q1d*N.x+q2d*N.y+q3d*N.z)\n",
    "b1=a.locatenew('b1',x1*A.x+y1*A.y)\n",
    "b2=a.locatenew('b2',x2*A.x+y2*A.y)\n",
    "b3=a.locatenew('b3',x3*A.x+y3*A.y)\n",
    "b4=a.locatenew('b4',x4*A.x+y4*A.y)\n",
    "b5=a.locatenew('b5',x5*A.x+y5*A.y)\n",
    "b6=a.locatenew('b6',x6*A.x+y6*A.y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{A2: Derivative(q6(t), t)*A2.x,\n",
       " B1: 0,\n",
       " B2: 0,\n",
       " B3: 0,\n",
       " B4: 0,\n",
       " B6: 0,\n",
       " B6: 0,\n",
       " A: - Derivative(q4(t), t)*N.z - Derivative(q5(t), t)*A1.y - Derivative(q6(t), t)*A2.x}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A._ang_vel_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Definicion de las fuerzas\n",
    "[f1,f2,f3,f4,f5,f6]=symbols('f1,f2,f3,f4,f5,f6')\n",
    "F1=getComponents(f1*B1.y,N)[0]*N.x+getComponents(f1*B1.y,N)[1]*N.y+getComponents(f1*B1.y,N)[2]*N.z\n",
    "F2=getComponents(f2*B2.y,N)[0]*N.x+getComponents(f2*B2.y,N)[1]*N.y+getComponents(f2*B2.y,N)[2]*N.z\n",
    "F3=getComponents(f3*B3.y,N)[0]*N.x+getComponents(f3*B3.y,N)[1]*N.y+getComponents(f3*B3.y,N)[2]*N.z\n",
    "F4=getComponents(f4*B4.y,N)[0]*N.x+getComponents(f4*B4.y,N)[1]*N.y+getComponents(f4*B4.y,N)[2]*N.z\n",
    "F5=getComponents(f5*B5.y,N)[0]*N.x+getComponents(f5*B5.y,N)[1]*N.y+getComponents(f5*B5.y,N)[2]*N.z\n",
    "F6=getComponents(f6*B6.y,N)[0]*N.x+getComponents(f6*B6.y,N)[1]*N.y+getComponents(f6*B6.y,N)[2]*N.z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Se define el cuerpo rigido\n",
    "inertia_sub=inertia(A,Ixx,Iyy,Izz)\n",
    "sub = RigidBody('S',a,A,m,(inertia_sub,a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - g m \\operatorname{q_{3}}{\\left(t \\right)}$"
      ],
      "text/plain": [
       "-g⋅m⋅q₃(t)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sub.potential_energy = -m*g*q3\n",
    "sub.potential_energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle Ixx\\mathbf{\\hat{a}_x}\\otimes \\mathbf{\\hat{a}_x} + Iyy\\mathbf{\\hat{a}_y}\\otimes \\mathbf{\\hat{a}_y} + Izz\\mathbf{\\hat{a}_z}\\otimes \\mathbf{\\hat{a}_z}$"
      ],
      "text/plain": [
       "Ixx a_x⊗a_x + Iyy a_y⊗a_y + Izz a_z⊗a_z"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inertia_sub"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle - Ixx \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} - \\frac{Ixx \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2}}{2} + \\frac{Ixx \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2}}{2} + \\frac{Ixx \\left(\\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)}\\right)^{2}}{2} + Iyy \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} - \\frac{Iyy \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2}}{2} + \\frac{Iyy \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2}}{2} + \\frac{Iyy \\cos^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)}\\right)^{2}}{2} - Izz \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} + \\frac{Izz \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2}}{2} - \\frac{Izz \\cos^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)}\\right)^{2}}{2} + \\frac{Izz \\left(\\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)}\\right)^{2}}{2} + g m \\operatorname{q_{3}}{\\left(t \\right)} + \\frac{m \\left(\\frac{d}{d t} \\operatorname{q_{1}}{\\left(t \\right)}\\right)^{2}}{2} + \\frac{m \\left(\\frac{d}{d t} \\operatorname{q_{2}}{\\left(t \\right)}\\right)^{2}}{2} + \\frac{m \\left(\\frac{d}{d t} \\operatorname{q_{3}}{\\left(t \\right)}\\right)^{2}}{2}$"
      ],
      "text/plain": [
       "                                                                  2           \n",
       "                                              2        ⎛d        ⎞        ⎛d  \n",
       "                                       Ixx⋅cos (q₅(t))⋅⎜──(q₄(t))⎟    Ixx⋅⎜──(\n",
       "                 d         d                           ⎝dt       ⎠        ⎝dt \n",
       "- Ixx⋅sin(q₅(t))⋅──(q₄(t))⋅──(q₆(t)) - ──────────────────────────── + ────────\n",
       "                 dt        dt                       2                        2\n",
       "\n",
       "       2                  2                                                   \n",
       "      ⎞        ⎛d        ⎞                                                    \n",
       "q₄(t))⎟    Ixx⋅⎜──(q₆(t))⎟                                                    \n",
       "      ⎠        ⎝dt       ⎠                                         d         d\n",
       "──────── + ──────────────── + Iyy⋅sin(q₆(t))⋅cos(q₅(t))⋅cos(q₆(t))⋅──(q₄(t))⋅─\n",
       "                  2                                                dt        d\n",
       "\n",
       "                                                  2                           \n",
       "                  2           2        ⎛d        ⎞           2        ⎛d      \n",
       "           Iyy⋅cos (q₅(t))⋅cos (q₆(t))⋅⎜──(q₄(t))⎟    Iyy⋅cos (q₅(t))⋅⎜──(q₄(t\n",
       "                                       ⎝dt       ⎠                    ⎝dt     \n",
       "─(q₅(t)) - ──────────────────────────────────────── + ────────────────────────\n",
       "t                             2                                    2          \n",
       "\n",
       "   2                              2                                           \n",
       "  ⎞           2        ⎛d        ⎞                                            \n",
       "))⎟    Iyy⋅cos (q₆(t))⋅⎜──(q₅(t))⎟                                            \n",
       "  ⎠                    ⎝dt       ⎠                                         d  \n",
       "──── + ──────────────────────────── - Izz⋅sin(q₆(t))⋅cos(q₅(t))⋅cos(q₆(t))⋅──(\n",
       "                    2                                                      dt \n",
       "\n",
       "                                                          2                   \n",
       "                          2           2        ⎛d        ⎞           2        \n",
       "                   Izz⋅cos (q₅(t))⋅cos (q₆(t))⋅⎜──(q₄(t))⎟    Izz⋅cos (q₆(t))⋅\n",
       "       d                                       ⎝dt       ⎠                    \n",
       "q₄(t))⋅──(q₅(t)) + ──────────────────────────────────────── - ────────────────\n",
       "       dt                             2                                    2  \n",
       "\n",
       "           2                  2                            2                2 \n",
       "⎛d        ⎞        ⎛d        ⎞                  ⎛d        ⎞      ⎛d        ⎞  \n",
       "⎜──(q₅(t))⎟    Izz⋅⎜──(q₅(t))⎟                m⋅⎜──(q₁(t))⎟    m⋅⎜──(q₂(t))⎟  \n",
       "⎝dt       ⎠        ⎝dt       ⎠                  ⎝dt       ⎠      ⎝dt       ⎠  \n",
       "──────────── + ──────────────── + g⋅m⋅q₃(t) + ────────────── + ────────────── \n",
       "                      2                             2                2        \n",
       "\n",
       "               2\n",
       "    ⎛d        ⎞ \n",
       "  m⋅⎜──(q₃(t))⎟ \n",
       "    ⎝dt       ⎠ \n",
       "+ ──────────────\n",
       "        2       "
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vel = q1d*N.x+q2d*N.y+q3d*N.z\n",
    "ang_vel = (q4d*N.z+q5d*A1.y+q6d*A2.x).express(N)\n",
    "T = sympy.simplify(sympy.Rational(1/2)*m*vel.dot(vel) + sympy.Rational(1/2)*ang_vel.dot(inertia_sub.express(N).dot(ang_vel)))\n",
    "V = -m*g*q3\n",
    "L = T - V\n",
    "L\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle \\frac{Ixx \\sin^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2}}{2} - Ixx \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} + \\frac{Ixx \\left(\\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)}\\right)^{2}}{2} + \\frac{Iyy \\left(- \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} - 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} + 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)}}{4} + \\frac{Iyy \\sin^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2}}{2} + \\frac{Iyy \\cos^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)}\\right)^{2}}{2} - \\frac{Izz \\left(- \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} - 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} + 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)}}{4} + \\frac{Izz \\sin^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)}\\right)^{2}}{2} + \\frac{Izz \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2}}{2} + g m \\operatorname{q_{3}}{\\left(t \\right)} + \\frac{m \\left(\\frac{d}{d t} \\operatorname{q_{1}}{\\left(t \\right)}\\right)^{2}}{2} + \\frac{m \\left(\\frac{d}{d t} \\operatorname{q_{2}}{\\left(t \\right)}\\right)^{2}}{2} + \\frac{m \\left(\\frac{d}{d t} \\operatorname{q_{3}}{\\left(t \\right)}\\right)^{2}}{2}$"
      ],
      "text/plain": [
       "                           2                                                  \n",
       "       2        ⎛d        ⎞                                             ⎛d    \n",
       "Ixx⋅sin (q₅(t))⋅⎜──(q₄(t))⎟                                         Ixx⋅⎜──(q₆\n",
       "                ⎝dt       ⎠                   d         d               ⎝dt   \n",
       "──────────────────────────── - Ixx⋅sin(q₅(t))⋅──(q₄(t))⋅──(q₆(t)) + ──────────\n",
       "             2                                dt        dt                 2  \n",
       "\n",
       "     2                                                                        \n",
       "    ⎞                                                       d         d       \n",
       "(t))⎟    Iyy⋅(-sin(q₅(t) - 2⋅q₆(t)) + sin(q₅(t) + 2⋅q₆(t)))⋅──(q₄(t))⋅──(q₅(t)\n",
       "    ⎠                                                       dt        dt      \n",
       "────── + ─────────────────────────────────────────────────────────────────────\n",
       "                                           4                                  \n",
       "\n",
       "                                           2                              2   \n",
       "           2           2        ⎛d        ⎞           2        ⎛d        ⎞    \n",
       ")   Iyy⋅sin (q₆(t))⋅cos (q₅(t))⋅⎜──(q₄(t))⎟    Iyy⋅cos (q₆(t))⋅⎜──(q₅(t))⎟    \n",
       "                                ⎝dt       ⎠                    ⎝dt       ⎠    \n",
       "─ + ──────────────────────────────────────── + ──────────────────────────── - \n",
       "                       2                                    2                 \n",
       "\n",
       "                                                                              \n",
       "                                                   d         d                \n",
       "Izz⋅(-sin(q₅(t) - 2⋅q₆(t)) + sin(q₅(t) + 2⋅q₆(t)))⋅──(q₄(t))⋅──(q₅(t))   Izz⋅s\n",
       "                                                   dt        dt               \n",
       "────────────────────────────────────────────────────────────────────── + ─────\n",
       "                                  4                                           \n",
       "\n",
       "                      2                                          2            \n",
       "  2        ⎛d        ⎞           2           2        ⎛d        ⎞             \n",
       "in (q₆(t))⋅⎜──(q₅(t))⎟    Izz⋅cos (q₅(t))⋅cos (q₆(t))⋅⎜──(q₄(t))⎟             \n",
       "           ⎝dt       ⎠                                ⎝dt       ⎠             \n",
       "─────────────────────── + ──────────────────────────────────────── + g⋅m⋅q₃(t)\n",
       "        2                                    2                                \n",
       "\n",
       "                2                2                2\n",
       "     ⎛d        ⎞      ⎛d        ⎞      ⎛d        ⎞ \n",
       "   m⋅⎜──(q₁(t))⎟    m⋅⎜──(q₂(t))⎟    m⋅⎜──(q₃(t))⎟ \n",
       "     ⎝dt       ⎠      ⎝dt       ⎠      ⎝dt       ⎠ \n",
       " + ────────────── + ────────────── + ──────────────\n",
       "         2                2                2       "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L=sympy.simplify(Lagrangian(N,sub))\n",
    "L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "ftuples = [(b1,F1),(b2,F2),(b3,F3),(b4,F4),(b5,F5),(b6,F6)]\n",
    "lm = LagrangesMethod(L,[q1,q2,q3,q4,q5,q6],ftuples,frame=N)\n",
    "eqs = lm.form_lagranges_equations()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "eqs.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}f_{1} \\left(\\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\beta_{1} \\right)} - \\sin{\\left(\\beta_{1} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) + f_{2} \\left(\\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\beta_{2} \\right)} + \\sin{\\left(\\beta_{2} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) + f_{3} \\left(\\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\beta_{3} \\right)} - \\sin{\\left(\\beta_{3} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) + f_{4} \\left(\\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\beta_{4} \\right)} + \\sin{\\left(\\beta_{4} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) - f_{5} \\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 6.12323399573677 \\cdot 10^{-17} \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 6.12323399573677 \\cdot 10^{-17} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} + \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) - f_{6} \\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 6.12323399573677 \\cdot 10^{-17} \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 6.12323399573677 \\cdot 10^{-17} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} + \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) + m \\frac{d^{2}}{d t^{2}} \\operatorname{q_{1}}{\\left(t \\right)}\\\\- f_{1} \\left(\\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\beta_{1} \\right)} + \\sin{\\left(\\beta_{1} \\right)} \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) - f_{2} \\left(\\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\beta_{2} \\right)} - \\sin{\\left(\\beta_{2} \\right)} \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) - f_{3} \\left(\\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\beta_{3} \\right)} + \\sin{\\left(\\beta_{3} \\right)} \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) - f_{4} \\left(\\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\beta_{4} \\right)} - \\sin{\\left(\\beta_{4} \\right)} \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) - f_{5} \\left(6.12323399573677 \\cdot 10^{-17} \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} + 6.12323399573677 \\cdot 10^{-17} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) - f_{6} \\left(6.12323399573677 \\cdot 10^{-17} \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} + 6.12323399573677 \\cdot 10^{-17} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) + m \\frac{d^{2}}{d t^{2}} \\operatorname{q_{2}}{\\left(t \\right)}\\\\f_{1} \\left(\\sin{\\left(\\beta_{1} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} - \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\beta_{1} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) - f_{2} \\left(\\sin{\\left(\\beta_{2} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} + \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\beta_{2} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) + f_{3} \\left(\\sin{\\left(\\beta_{3} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} - \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\beta_{3} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) - f_{4} \\left(\\sin{\\left(\\beta_{4} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} + \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\beta_{4} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) - f_{5} \\left(6.12323399573677 \\cdot 10^{-17} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} - f_{6} \\left(6.12323399573677 \\cdot 10^{-17} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} - g m + m \\frac{d^{2}}{d t^{2}} \\operatorname{q_{3}}{\\left(t \\right)}\\\\2.0 Ixx \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} - 1.0 Ixx \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{q_{6}}{\\left(t \\right)} - 1.0 Ixx \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{q_{4}}{\\left(t \\right)} - 1.0 Ixx \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} + 1.0 Ixx \\frac{d^{2}}{d t^{2}} \\operatorname{q_{4}}{\\left(t \\right)} - 1.0 Iyy \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)}\\right)^{2} + 2.0 Iyy \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} - 2.0 Iyy \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} + 2.0 Iyy \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} + 1.0 Iyy \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{q_{5}}{\\left(t \\right)} - 1.0 Iyy \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{q_{4}}{\\left(t \\right)} + 1.0 Iyy \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{q_{4}}{\\left(t \\right)} + 2.0 Iyy \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} - 1.0 Iyy \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} + 1.0 Izz \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)}\\right)^{2} - 2.0 Izz \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} - 2.0 Izz \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} - 1.0 Izz \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{q_{5}}{\\left(t \\right)} + 1.0 Izz \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{q_{4}}{\\left(t \\right)} - 2.0 Izz \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} + 1.0 Izz \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} - 1.0 f_{1} x_{1} \\cos{\\left(\\beta_{1} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 1.0 f_{1} y_{1} \\sin{\\left(\\beta_{1} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 1.0 f_{2} x_{2} \\cos{\\left(\\beta_{2} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 1.0 f_{2} y_{2} \\sin{\\left(\\beta_{2} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 1.0 f_{3} x_{3} \\cos{\\left(\\beta_{3} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 1.0 f_{3} y_{3} \\sin{\\left(\\beta_{3} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 1.0 f_{4} x_{4} \\cos{\\left(\\beta_{4} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 1.0 f_{4} y_{4} \\sin{\\left(\\beta_{4} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 1.0 f_{5} x_{5} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} - 6.12323399573677 \\cdot 10^{-17} f_{5} x_{5} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 1.0 f_{5} y_{5} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} + 1.0 f_{6} x_{6} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} - 6.12323399573677 \\cdot 10^{-17} f_{6} x_{6} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 1.0 f_{6} y_{6} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\\\- 0.5 Ixx \\sin{\\left(2 \\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2} + 1.0 Ixx \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} - 0.25 Iyy \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} - 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{q_{4}}{\\left(t \\right)} + 0.25 Iyy \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} + 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{q_{4}}{\\left(t \\right)} - 0.125 Iyy \\sin{\\left(2 \\operatorname{q_{5}}{\\left(t \\right)} - 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2} - 0.125 Iyy \\sin{\\left(2 \\operatorname{q_{5}}{\\left(t \\right)} + 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2} + 0.25 Iyy \\sin{\\left(2 \\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2} - 1.0 Iyy \\sin{\\left(2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} + 0.5 Iyy \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} - 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} + 0.5 Iyy \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} + 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} + 0.5 Iyy \\cos{\\left(2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{q_{5}}{\\left(t \\right)} + 0.5 Iyy \\frac{d^{2}}{d t^{2}} \\operatorname{q_{5}}{\\left(t \\right)} + 0.25 Izz \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} - 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{q_{4}}{\\left(t \\right)} - 0.25 Izz \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} + 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{q_{4}}{\\left(t \\right)} + 0.125 Izz \\sin{\\left(2 \\operatorname{q_{5}}{\\left(t \\right)} - 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2} + 0.125 Izz \\sin{\\left(2 \\operatorname{q_{5}}{\\left(t \\right)} + 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2} + 0.25 Izz \\sin{\\left(2 \\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2} + 1.0 Izz \\sin{\\left(2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} - 0.5 Izz \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} - 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} - 0.5 Izz \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} + 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} - 0.5 Izz \\cos{\\left(2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{q_{5}}{\\left(t \\right)} + 0.5 Izz \\frac{d^{2}}{d t^{2}} \\operatorname{q_{5}}{\\left(t \\right)} - 0.5 f_{1} x_{1} \\sin{\\left(\\beta_{1} - \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 0.5 f_{1} x_{1} \\sin{\\left(\\beta_{1} + \\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 0.5 f_{1} y_{1} \\cos{\\left(\\beta_{1} - \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 0.5 f_{1} y_{1} \\cos{\\left(\\beta_{1} + \\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 0.5 f_{2} x_{2} \\sin{\\left(\\beta_{2} - \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 0.5 f_{2} x_{2} \\sin{\\left(\\beta_{2} + \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 0.5 f_{2} y_{2} \\cos{\\left(\\beta_{2} - \\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 0.5 f_{2} y_{2} \\cos{\\left(\\beta_{2} + \\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 0.5 f_{3} x_{3} \\sin{\\left(\\beta_{3} - \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 0.5 f_{3} x_{3} \\sin{\\left(\\beta_{3} + \\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 0.5 f_{3} y_{3} \\cos{\\left(\\beta_{3} - \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 0.5 f_{3} y_{3} \\cos{\\left(\\beta_{3} + \\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 0.5 f_{4} x_{4} \\sin{\\left(\\beta_{4} - \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 0.5 f_{4} x_{4} \\sin{\\left(\\beta_{4} + \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 0.5 f_{4} y_{4} \\cos{\\left(\\beta_{4} - \\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 0.5 f_{4} y_{4} \\cos{\\left(\\beta_{4} + \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 6.12323399573677 \\cdot 10^{-17} f_{5} x_{5} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 1.0 f_{5} x_{5} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 6.12323399573677 \\cdot 10^{-17} f_{6} x_{6} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 1.0 f_{6} x_{6} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\\\- Ixx \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{q_{4}}{\\left(t \\right)} - Ixx \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} + Ixx \\frac{d^{2}}{d t^{2}} \\operatorname{q_{6}}{\\left(t \\right)} + Iyy \\left(2 \\sin^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 1\\right) \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} - Iyy \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2} + \\frac{Iyy \\sin{\\left(2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)}\\right)^{2}}{2} - Izz \\left(2 \\sin^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 1\\right) \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} + Izz \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2} - \\frac{Izz \\sin{\\left(2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)}\\right)^{2}}{2} - 1.0 f_{5} y_{5} - 1.0 f_{6} y_{6}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
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       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                     2       \n",
       "⎢                              d         d                           d        \n",
       "⎢2.0⋅Ixx⋅sin(q₅(t))⋅cos(q₅(t))⋅──(q₄(t))⋅──(q₅(t)) - Ixx⋅sin(q₅(t))⋅───(q₆(t))\n",
       "⎢                              dt        dt                           2       \n",
       "⎢                                                                   dt        \n",
       "⎢                                                                             \n",
       "⎢                                                 2                           \n",
       "⎢                                      ⎛d        ⎞                       d    \n",
       "⎢               - 0.5⋅Ixx⋅sin(2⋅q₅(t))⋅⎜──(q₄(t))⎟  + 1.0⋅Ixx⋅cos(q₅(t))⋅──(q₄\n",
       "⎢                                      ⎝dt       ⎠                       dt   \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎣                                                                             \n",
       "\n",
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       "                     2                                                        \n",
       "          2         d                          d         d                    \n",
       " - Ixx⋅cos (q₅(t))⋅───(q₄(t)) - Ixx⋅cos(q₅(t))⋅──(q₅(t))⋅──(q₆(t)) + 1.0⋅Ixx⋅─\n",
       "                     2                         dt        dt                   \n",
       "                   dt                                                        d\n",
       "                                                                              \n",
       "                                                 2                            \n",
       "     d                                          d                             \n",
       "(t))⋅──(q₆(t)) - 0.25⋅Iyy⋅sin(q₅(t) - 2⋅q₆(t))⋅───(q₄(t)) + 0.25⋅Iyy⋅sin(q₅(t)\n",
       "     dt                                          2                            \n",
       "                                               dt                             \n",
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       "\n",
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       "                                                                              \n",
       " 2                                                          2                 \n",
       "d                                                ⎛d        ⎞                  \n",
       "──(q₄(t)) - Iyy⋅sin(q₅(t))⋅sin(q₆(t))⋅cos(q₆(t))⋅⎜──(q₅(t))⎟  + 2.0⋅Iyy⋅sin(q₅\n",
       " 2                                               ⎝dt       ⎠                  \n",
       "t                                                                             \n",
       "                                                                              \n",
       "              2                                                      2        \n",
       "             d                                            ⎛d        ⎞         \n",
       " + 2⋅q₆(t))⋅───(q₄(t)) - 0.125⋅Iyy⋅sin(2⋅q₅(t) - 2⋅q₆(t))⋅⎜──(q₄(t))⎟  - 0.125\n",
       "              2                                           ⎝dt       ⎠         \n",
       "            dt                                                                \n",
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       "\n",
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       "                                                                              \n",
       "                                                                              \n",
       "                   2        d         d                                       \n",
       "(t))⋅cos(q₅(t))⋅cos (q₆(t))⋅──(q₄(t))⋅──(q₅(t)) - 2.0⋅Iyy⋅sin(q₅(t))⋅cos(q₅(t)\n",
       "                            dt        dt                                      \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                       2                                    2 \n",
       "                            ⎛d        ⎞                          ⎛d        ⎞  \n",
       "⋅Iyy⋅sin(2⋅q₅(t) + 2⋅q₆(t))⋅⎜──(q₄(t))⎟  + 0.25⋅Iyy⋅sin(2⋅q₅(t))⋅⎜──(q₄(t))⎟  \n",
       "                            ⎝dt       ⎠                          ⎝dt       ⎠  \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
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       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                               f₁⋅((sin(q₄(t))\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                               -f₁⋅((sin(q₄(t)\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "  d         d                                 2                   d         d \n",
       ")⋅──(q₄(t))⋅──(q₅(t)) + 2.0⋅Iyy⋅sin(q₆(t))⋅cos (q₅(t))⋅cos(q₆(t))⋅──(q₄(t))⋅──\n",
       "  dt        dt                                                    dt        dt\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                   d         d                                        d       \n",
       "- Iyy⋅sin(2⋅q₆(t))⋅──(q₅(t))⋅──(q₆(t)) + 0.5⋅Iyy⋅cos(q₅(t) - 2⋅q₆(t))⋅──(q₄(t)\n",
       "                   dt        dt                                       dt      \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "⋅cos(q₆(t)) - sin(q₅(t))⋅sin(q₆(t))⋅cos(q₄(t)))⋅cos(β₁) - sin(β₁)⋅cos(q₄(t))⋅c\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       ")⋅sin(q₅(t))⋅sin(q₆(t)) + cos(q₄(t))⋅cos(q₆(t)))⋅cos(β₁) + sin(β₁)⋅sin(q₄(t))⋅\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                     2                        \n",
       "                                                    d                  2      \n",
       "(q₆(t)) + 1.0⋅Iyy⋅sin(q₆(t))⋅cos(q₅(t))⋅cos(q₆(t))⋅───(q₅(t)) - Iyy⋅cos (q₅(t)\n",
       "                                                     2                        \n",
       "                                                   dt                         \n",
       "                                                                              \n",
       "                                                                              \n",
       "  d                                        d         d                        \n",
       ")⋅──(q₆(t)) + 0.5⋅Iyy⋅cos(q₅(t) + 2⋅q₆(t))⋅──(q₄(t))⋅──(q₆(t)) + 0.5⋅Iyy⋅cos(2\n",
       "  dt                                       dt        dt                       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "os(q₅(t))) + f₂⋅((sin(q₄(t))⋅cos(q₆(t)) - sin(q₅(t))⋅sin(q₆(t))⋅cos(q₄(t)))⋅co\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "cos(q₅(t))) - f₂⋅((sin(q₄(t))⋅sin(q₅(t))⋅sin(q₆(t)) + cos(q₄(t))⋅cos(q₆(t)))⋅c\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                2                                2                            \n",
       "     2         d                      2         d                             \n",
       ")⋅cos (q₆(t))⋅───(q₄(t)) + 1.0⋅Iyy⋅cos (q₅(t))⋅───(q₄(t)) + 2.0⋅Iyy⋅cos(q₅(t))\n",
       "                2                                2                            \n",
       "              dt                               dt                             \n",
       "                                                                              \n",
       "          2                    2                                          2   \n",
       "         d                    d                                          d    \n",
       "⋅q₆(t))⋅───(q₅(t)) + 0.5⋅Iyy⋅───(q₅(t)) + 0.25⋅Izz⋅sin(q₅(t) - 2⋅q₆(t))⋅───(q₄\n",
       "          2                    2                                          2   \n",
       "        dt                   dt                                         dt    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "s(β₂) + sin(β₂)⋅cos(q₄(t))⋅cos(q₅(t))) + f₃⋅((sin(q₄(t))⋅cos(q₆(t)) - sin(q₅(t\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "os(β₂) - sin(β₂)⋅sin(q₄(t))⋅cos(q₅(t))) - f₃⋅((sin(q₄(t))⋅sin(q₅(t))⋅sin(q₆(t)\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                        f₁⋅(sin(β₁)⋅sin(q₅(t)) - sin(q₆(t))⋅cos(β₁)⋅cos(q₅(t))\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "    2        d         d                          d         d                 \n",
       "⋅cos (q₆(t))⋅──(q₅(t))⋅──(q₆(t)) - Iyy⋅cos(q₅(t))⋅──(q₅(t))⋅──(q₆(t)) + 1.0⋅Iz\n",
       "             dt        dt                         dt        dt                \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                       2                                      \n",
       "                                      d                                       \n",
       "(t)) - 0.25⋅Izz⋅sin(q₅(t) + 2⋅q₆(t))⋅───(q₄(t)) + 0.125⋅Izz⋅sin(2⋅q₅(t) - 2⋅q₆\n",
       "                                       2                                      \n",
       "                                     dt                                       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                         2                                    \n",
       "                                        d                          d         d\n",
       "                      - Ixx⋅sin(q₅(t))⋅───(q₄(t)) - Ixx⋅cos(q₅(t))⋅──(q₄(t))⋅─\n",
       "                                         2                         dt        d\n",
       "                                       dt                                     \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "))⋅sin(q₆(t))⋅cos(q₄(t)))⋅cos(β₃) - sin(β₃)⋅cos(q₄(t))⋅cos(q₅(t))) + f₄⋅((sin(\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       ") + cos(q₄(t))⋅cos(q₆(t)))⋅cos(β₃) + sin(β₃)⋅sin(q₄(t))⋅cos(q₅(t))) - f₄⋅((sin\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       ") - f₂⋅(sin(β₂)⋅sin(q₅(t)) + sin(q₆(t))⋅cos(β₂)⋅cos(q₅(t))) + f₃⋅(sin(β₃)⋅sin(\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                              2                               \n",
       "                                   ⎛d        ⎞                                \n",
       "z⋅sin(q₅(t))⋅sin(q₆(t))⋅cos(q₆(t))⋅⎜──(q₅(t))⎟  - 2.0⋅Izz⋅sin(q₅(t))⋅cos(q₅(t)\n",
       "                                   ⎝dt       ⎠                                \n",
       "                                                                              \n",
       "                                                                              \n",
       "                2                                               2             \n",
       "     ⎛d        ⎞                                     ⎛d        ⎞              \n",
       "(t))⋅⎜──(q₄(t))⎟  + 0.125⋅Izz⋅sin(2⋅q₅(t) + 2⋅q₆(t))⋅⎜──(q₄(t))⎟  + 0.25⋅Izz⋅s\n",
       "     ⎝dt       ⎠                                     ⎝dt       ⎠              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                 2                                                            \n",
       "                d               ⎛     2           ⎞            d         d    \n",
       "─(q₅(t)) + Ixx⋅───(q₆(t)) + Iyy⋅⎝2⋅sin (q₆(t)) - 1⎠⋅cos(q₅(t))⋅──(q₄(t))⋅──(q₅\n",
       "t                2                                             dt        dt   \n",
       "               dt                                                             \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "q₄(t))⋅cos(q₆(t)) - sin(q₅(t))⋅sin(q₆(t))⋅cos(q₄(t)))⋅cos(β₄) + sin(β₄)⋅cos(q₄\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "(q₄(t))⋅sin(q₅(t))⋅sin(q₆(t)) + cos(q₄(t))⋅cos(q₆(t)))⋅cos(β₄) - sin(β₄)⋅sin(q\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "q₅(t)) - sin(q₆(t))⋅cos(β₃)⋅cos(q₅(t))) - f₄⋅(sin(β₄)⋅sin(q₅(t)) + sin(q₆(t))⋅\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "     2        d         d                                 2                   \n",
       ")⋅cos (q₆(t))⋅──(q₄(t))⋅──(q₅(t)) - 2.0⋅Izz⋅sin(q₆(t))⋅cos (q₅(t))⋅cos(q₆(t))⋅\n",
       "              dt        dt                                                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                       2                                                      \n",
       "            ⎛d        ⎞                         d         d                   \n",
       "in(2⋅q₅(t))⋅⎜──(q₄(t))⎟  + 1.0⋅Izz⋅sin(2⋅q₆(t))⋅──(q₅(t))⋅──(q₆(t)) - 0.5⋅Izz⋅\n",
       "            ⎝dt       ⎠                         dt        dt                  \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                             ⎛\n",
       "                                                        2   Iyy⋅sin(2⋅q₆(t))⋅⎜\n",
       "                         2                   ⎛d        ⎞                     ⎝\n",
       "(t)) - Iyy⋅sin(q₆(t))⋅cos (q₅(t))⋅cos(q₆(t))⋅⎜──(q₄(t))⎟  + ──────────────────\n",
       "                                             ⎝dt       ⎠                  2   \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "(t))⋅cos(q₅(t))) - f₅⋅(sin(q₄(t))⋅sin(q₆(t)) - 6.12323399573677e-17⋅sin(q₄(t))\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "₄(t))⋅cos(q₅(t))) - f₅⋅(6.12323399573677e-17⋅sin(q₄(t))⋅sin(q₅(t))⋅sin(q₆(t)) \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "cos(β₄)⋅cos(q₅(t))) - f₅⋅(6.12323399573677e-17⋅sin(q₆(t)) + cos(q₆(t)))⋅cos(q₅\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                             2                \n",
       "d         d                                                 d                 \n",
       "──(q₄(t))⋅──(q₆(t)) - Izz⋅sin(q₆(t))⋅cos(q₅(t))⋅cos(q₆(t))⋅───(q₅(t)) + 1.0⋅Iz\n",
       "dt        dt                                                 2                \n",
       "                                                           dt                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "                     d         d                                        d     \n",
       "cos(q₅(t) - 2⋅q₆(t))⋅──(q₄(t))⋅──(q₆(t)) - 0.5⋅Izz⋅cos(q₅(t) + 2⋅q₆(t))⋅──(q₄(\n",
       "                     dt        dt                                       dt    \n",
       "                                                                              \n",
       "                                                                              \n",
       "          2                                                                   \n",
       "d        ⎞                                                                    \n",
       "──(q₅(t))⎟                                                                    \n",
       "dt       ⎠        ⎛     2           ⎞            d         d                  \n",
       "─────────── - Izz⋅⎝2⋅sin (q₆(t)) - 1⎠⋅cos(q₅(t))⋅──(q₄(t))⋅──(q₅(t)) + Izz⋅sin\n",
       "                                                 dt        dt                 \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "⋅cos(q₆(t)) + 6.12323399573677e-17⋅sin(q₅(t))⋅sin(q₆(t))⋅cos(q₄(t)) + sin(q₅(t\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "+ sin(q₄(t))⋅sin(q₅(t))⋅cos(q₆(t)) - sin(q₆(t))⋅cos(q₄(t)) + 6.12323399573677e\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "(t)) - f₆⋅(6.12323399573677e-17⋅sin(q₆(t)) + cos(q₆(t)))⋅cos(q₅(t)) - g⋅m + m⋅\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                            2                                                 \n",
       "     2           2         d                                 2        d       \n",
       "z⋅cos (q₅(t))⋅cos (q₆(t))⋅───(q₄(t)) - 2.0⋅Izz⋅cos(q₅(t))⋅cos (q₆(t))⋅──(q₅(t)\n",
       "                            2                                         dt      \n",
       "                          dt                                                  \n",
       "                                                                              \n",
       "                                       2                    2                 \n",
       "    d                                 d                    d                  \n",
       "t))⋅──(q₆(t)) - 0.5⋅Izz⋅cos(2⋅q₆(t))⋅───(q₅(t)) + 0.5⋅Izz⋅───(q₅(t)) - 0.5⋅f₁⋅\n",
       "    dt                                 2                    2                 \n",
       "                                     dt                   dt                  \n",
       "                                                                              \n",
       "                                                                          2   \n",
       "                                                               ⎛d        ⎞    \n",
       "                                          2   Izz⋅sin(2⋅q₆(t))⋅⎜──(q₅(t))⎟    \n",
       "           2                   ⎛d        ⎞                     ⎝dt       ⎠    \n",
       "(q₆(t))⋅cos (q₅(t))⋅cos(q₆(t))⋅⎜──(q₄(t))⎟  - ───────────────────────────── - \n",
       "                               ⎝dt       ⎠                  2                 \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "))⋅cos(q₄(t))⋅cos(q₆(t))) - f₆⋅(sin(q₄(t))⋅sin(q₆(t)) - 6.12323399573677e-17⋅s\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "-17⋅cos(q₄(t))⋅cos(q₆(t))) - f₆⋅(6.12323399573677e-17⋅sin(q₄(t))⋅sin(q₅(t))⋅si\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "  2                                                                           \n",
       " d                                                                            \n",
       "───(q₃(t))                                                                    \n",
       "  2                                                                           \n",
       "dt                                                                            \n",
       "                                                                              \n",
       "                                                                              \n",
       "  d                              d         d                                  \n",
       ")⋅──(q₆(t)) + 1.0⋅Izz⋅cos(q₅(t))⋅──(q₅(t))⋅──(q₆(t)) - f₁⋅x₁⋅cos(β₁)⋅cos(q₅(t)\n",
       "  dt                             dt        dt                                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "x₁⋅sin(β₁ - q₆(t)) + 0.5⋅f₁⋅x₁⋅sin(β₁ + q₆(t)) - 0.5⋅f₁⋅y₁⋅cos(β₁ - q₆(t)) + 0\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "f₅⋅y₅ - f₆⋅y₆                                                                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "in(q₄(t))⋅cos(q₆(t)) + 6.12323399573677e-17⋅sin(q₅(t))⋅sin(q₆(t))⋅cos(q₄(t)) +\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "n(q₆(t)) + sin(q₄(t))⋅sin(q₅(t))⋅cos(q₆(t)) - sin(q₆(t))⋅cos(q₄(t)) + 6.123233\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       ")⋅cos(q₆(t)) + 1.0⋅f₁⋅y₁⋅sin(β₁)⋅cos(q₅(t))⋅cos(q₆(t)) - f₂⋅x₂⋅cos(β₂)⋅cos(q₅(\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       ".5⋅f₁⋅y₁⋅cos(β₁ + q₆(t)) - 0.5⋅f₂⋅x₂⋅sin(β₂ - q₆(t)) + 0.5⋅f₂⋅x₂⋅sin(β₂ + q₆(t\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                         2                                    \n",
       "                                        d                                     \n",
       " sin(q₅(t))⋅cos(q₄(t))⋅cos(q₆(t))) + m⋅───(q₁(t))                             \n",
       "                                         2                                    \n",
       "                                       dt                                     \n",
       "                                                                              \n",
       "                                          2                                   \n",
       "                                         d                                    \n",
       "99573677e-17⋅cos(q₄(t))⋅cos(q₆(t))) + m⋅───(q₂(t))                            \n",
       "                                          2                                   \n",
       "                                        dt                                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "t))⋅cos(q₆(t)) - f₂⋅y₂⋅sin(β₂)⋅cos(q₅(t))⋅cos(q₆(t)) - f₃⋅x₃⋅cos(β₃)⋅cos(q₅(t)\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       ")) + 0.5⋅f₂⋅y₂⋅cos(β₂ - q₆(t)) - 0.5⋅f₂⋅y₂⋅cos(β₂ + q₆(t)) - 0.5⋅f₃⋅x₃⋅sin(β₃ \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       ")⋅cos(q₆(t)) + 1.0⋅f₃⋅y₃⋅sin(β₃)⋅cos(q₅(t))⋅cos(q₆(t)) - f₄⋅x₄⋅cos(β₄)⋅cos(q₅(\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "- q₆(t)) + 0.5⋅f₃⋅x₃⋅sin(β₃ + q₆(t)) - 0.5⋅f₃⋅y₃⋅cos(β₃ - q₆(t)) + 0.5⋅f₃⋅y₃⋅c\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "t))⋅cos(q₆(t)) - f₄⋅y₄⋅sin(β₄)⋅cos(q₅(t))⋅cos(q₆(t)) + 1.0⋅f₅⋅x₅⋅sin(q₆(t))⋅co\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "os(β₃ + q₆(t)) - 0.5⋅f₄⋅x₄⋅sin(β₄ - q₆(t)) + 0.5⋅f₄⋅x₄⋅sin(β₄ + q₆(t)) + 0.5⋅f\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "s(q₅(t)) - 6.12323399573677e-17⋅f₅⋅x₅⋅cos(q₅(t))⋅cos(q₆(t)) + 1.0⋅f₅⋅y₅⋅sin(q₅\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "₄⋅y₄⋅cos(β₄ - q₆(t)) - 0.5⋅f₄⋅y₄⋅cos(β₄ + q₆(t)) + 6.12323399573677e-17⋅f₅⋅x₅⋅\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "(t)) + 1.0⋅f₆⋅x₆⋅sin(q₆(t))⋅cos(q₅(t)) - 6.12323399573677e-17⋅f₆⋅x₆⋅cos(q₅(t))\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "sin(q₆(t)) + 1.0⋅f₅⋅x₅⋅cos(q₆(t)) + 6.12323399573677e-17⋅f₆⋅x₆⋅sin(q₆(t)) + 1.\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                  ⎤\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "⋅cos(q₆(t)) + 1.0⋅f₆⋅y₆⋅sin(q₅(t))⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "0⋅f₆⋅x₆⋅cos(q₆(t))                ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎥\n",
       "                                  ⎦"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eqs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{array}{cccccccccccc}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & m & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & m & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & m & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & Ixx \\sin^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} + Iyy \\sin^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} + Izz \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} & \\frac{Iyy \\left(- \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} - 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} + 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right)}{4} - \\frac{Izz \\left(- \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} - 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} + 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right)}{4} & - Ixx \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{Iyy \\left(- \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} - 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} + 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right)}{4} - \\frac{Izz \\left(- \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} - 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} + 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right)}{4} & Iyy \\cos^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + Izz \\sin^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & - Ixx \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} & 0 & Ixx\\end{array}\\right]$"
      ],
      "text/plain": [
       "⎡1  0  0  0  0  0  0  0  0                                                    \n",
       "⎢                                                                             \n",
       "⎢0  1  0  0  0  0  0  0  0                                                    \n",
       "⎢                                                                             \n",
       "⎢0  0  1  0  0  0  0  0  0                                                    \n",
       "⎢                                                                             \n",
       "⎢0  0  0  1  0  0  0  0  0                                                    \n",
       "⎢                                                                             \n",
       "⎢0  0  0  0  1  0  0  0  0                                                    \n",
       "⎢                                                                             \n",
       "⎢0  0  0  0  0  1  0  0  0                                                    \n",
       "⎢                                                                             \n",
       "⎢0  0  0  0  0  0  m  0  0                                                    \n",
       "⎢                                                                             \n",
       "⎢0  0  0  0  0  0  0  m  0                                                    \n",
       "⎢                                                                             \n",
       "⎢0  0  0  0  0  0  0  0  m                                                    \n",
       "⎢                                                                             \n",
       "⎢                                                2                 2          \n",
       "⎢0  0  0  0  0  0  0  0  0                Ixx⋅sin (q₅(t)) + Iyy⋅sin (q₆(t))⋅co\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                           Iyy⋅(-sin(q₅(t) - 2⋅q₆(t)) + sin(q₅(t) + 2⋅q₆(t)))\n",
       "⎢0  0  0  0  0  0  0  0  0  ──────────────────────────────────────────────────\n",
       "⎢                                                   4                         \n",
       "⎢                                                                             \n",
       "⎣0  0  0  0  0  0  0  0  0                                              -Ixx⋅s\n",
       "\n",
       " 0                                                                            \n",
       "                                                                              \n",
       " 0                                                                            \n",
       "                                                                              \n",
       " 0                                                                            \n",
       "                                                                              \n",
       " 0                                                                            \n",
       "                                                                              \n",
       " 0                                                                            \n",
       "                                                                              \n",
       " 0                                                                            \n",
       "                                                                              \n",
       " 0                                                                            \n",
       "                                                                              \n",
       " 0                                                                            \n",
       "                                                                              \n",
       " 0                                                                            \n",
       "                                                                              \n",
       " 2                 2           2                       Iyy⋅(-sin(q₅(t) - 2⋅q₆(\n",
       "s (q₅(t)) + Izz⋅cos (q₅(t))⋅cos (q₆(t))                ───────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "   Izz⋅(-sin(q₅(t) - 2⋅q₆(t)) + sin(q₅(t) + 2⋅q₆(t)))                         \n",
       " - ──────────────────────────────────────────────────                         \n",
       "                           4                                                  \n",
       "                                                                              \n",
       "in(q₅(t))                                                                     \n",
       "\n",
       "                            0                                                 \n",
       "                                                                              \n",
       "                            0                                                 \n",
       "                                                                              \n",
       "                            0                                                 \n",
       "                                                                              \n",
       "                            0                                                 \n",
       "                                                                              \n",
       "                            0                                                 \n",
       "                                                                              \n",
       "                            0                                                 \n",
       "                                                                              \n",
       "                            0                                                 \n",
       "                                                                              \n",
       "                            0                                                 \n",
       "                                                                              \n",
       "                            0                                                 \n",
       "                                                                              \n",
       "t)) + sin(q₅(t) + 2⋅q₆(t)))   Izz⋅(-sin(q₅(t) - 2⋅q₆(t)) + sin(q₅(t) + 2⋅q₆(t)\n",
       "─────────────────────────── - ────────────────────────────────────────────────\n",
       " 4                                                    4                       \n",
       "                                                                              \n",
       "                   2                 2                                        \n",
       "            Iyy⋅cos (q₆(t)) + Izz⋅sin (q₆(t))                                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "                            0                                                 \n",
       "\n",
       "           0       ⎤\n",
       "                   ⎥\n",
       "           0       ⎥\n",
       "                   ⎥\n",
       "           0       ⎥\n",
       "                   ⎥\n",
       "           0       ⎥\n",
       "                   ⎥\n",
       "           0       ⎥\n",
       "                   ⎥\n",
       "           0       ⎥\n",
       "                   ⎥\n",
       "           0       ⎥\n",
       "                   ⎥\n",
       "           0       ⎥\n",
       "                   ⎥\n",
       "           0       ⎥\n",
       "                   ⎥\n",
       "))                 ⎥\n",
       "──  -Ixx⋅sin(q₅(t))⎥\n",
       "                   ⎥\n",
       "                   ⎥\n",
       "                   ⎥\n",
       "           0       ⎥\n",
       "                   ⎥\n",
       "                   ⎥\n",
       "          Ixx      ⎦"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.mass_matrix_full"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{d}{d t} \\operatorname{q_{1}}{\\left(t \\right)}\\\\\\frac{d}{d t} \\operatorname{q_{2}}{\\left(t \\right)}\\\\\\frac{d}{d t} \\operatorname{q_{3}}{\\left(t \\right)}\\\\\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\\\\\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)}\\\\\\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)}\\\\- f_{1} \\left(\\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\beta_{1} \\right)} - \\sin{\\left(\\beta_{1} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) - f_{2} \\left(\\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\beta_{2} \\right)} + \\sin{\\left(\\beta_{2} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) - f_{3} \\left(\\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\beta_{3} \\right)} - \\sin{\\left(\\beta_{3} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) - f_{4} \\left(\\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\beta_{4} \\right)} + \\sin{\\left(\\beta_{4} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) + f_{5} \\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 6.12323399573677 \\cdot 10^{-17} \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 6.12323399573677 \\cdot 10^{-17} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} + \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) + f_{6} \\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 6.12323399573677 \\cdot 10^{-17} \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 6.12323399573677 \\cdot 10^{-17} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} + \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right)\\\\f_{1} \\left(\\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\beta_{1} \\right)} + \\sin{\\left(\\beta_{1} \\right)} \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) + f_{2} \\left(\\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\beta_{2} \\right)} - \\sin{\\left(\\beta_{2} \\right)} \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) + f_{3} \\left(\\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\beta_{3} \\right)} + \\sin{\\left(\\beta_{3} \\right)} \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) + f_{4} \\left(\\left(\\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\beta_{4} \\right)} - \\sin{\\left(\\beta_{4} \\right)} \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) + f_{5} \\left(6.12323399573677 \\cdot 10^{-17} \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} + 6.12323399573677 \\cdot 10^{-17} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) + f_{6} \\left(6.12323399573677 \\cdot 10^{-17} \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\sin{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} + 6.12323399573677 \\cdot 10^{-17} \\cos{\\left(\\operatorname{q_{4}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right)\\\\- f_{1} \\left(\\sin{\\left(\\beta_{1} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} - \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\beta_{1} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) + f_{2} \\left(\\sin{\\left(\\beta_{2} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} + \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\beta_{2} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) - f_{3} \\left(\\sin{\\left(\\beta_{3} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} - \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\beta_{3} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) + f_{4} \\left(\\sin{\\left(\\beta_{4} \\right)} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} + \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\beta_{4} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\right) + f_{5} \\left(6.12323399573677 \\cdot 10^{-17} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} + f_{6} \\left(6.12323399573677 \\cdot 10^{-17} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} + g m\\\\- 2.0 Ixx \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} + 1.0 Ixx \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} + 1.0 Iyy \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)}\\right)^{2} - 2.0 Iyy \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} + 2.0 Iyy \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} - 2.0 Iyy \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} - 2.0 Iyy \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} + 1.0 Iyy \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} - 1.0 Izz \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)}\\right)^{2} + 2.0 Izz \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} + 2.0 Izz \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} + 2.0 Izz \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} - 1.0 Izz \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} + 1.0 f_{1} x_{1} \\cos{\\left(\\beta_{1} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 1.0 f_{1} y_{1} \\sin{\\left(\\beta_{1} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 1.0 f_{2} x_{2} \\cos{\\left(\\beta_{2} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 1.0 f_{2} y_{2} \\sin{\\left(\\beta_{2} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 1.0 f_{3} x_{3} \\cos{\\left(\\beta_{3} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 1.0 f_{3} y_{3} \\sin{\\left(\\beta_{3} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 1.0 f_{4} x_{4} \\cos{\\left(\\beta_{4} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 1.0 f_{4} y_{4} \\sin{\\left(\\beta_{4} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 1.0 f_{5} x_{5} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} + 6.12323399573677 \\cdot 10^{-17} f_{5} x_{5} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 1.0 f_{5} y_{5} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} - 1.0 f_{6} x_{6} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} + 6.12323399573677 \\cdot 10^{-17} f_{6} x_{6} \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 1.0 f_{6} y_{6} \\sin{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)}\\\\0.5 Ixx \\sin{\\left(2 \\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2} - 1.0 Ixx \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} + 0.125 Iyy \\sin{\\left(2 \\operatorname{q_{5}}{\\left(t \\right)} - 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2} + 0.125 Iyy \\sin{\\left(2 \\operatorname{q_{5}}{\\left(t \\right)} + 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2} - 0.25 Iyy \\sin{\\left(2 \\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2} + 1.0 Iyy \\sin{\\left(2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} - 0.5 Iyy \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} - 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} - 0.5 Iyy \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} + 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} - 0.125 Izz \\sin{\\left(2 \\operatorname{q_{5}}{\\left(t \\right)} - 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2} - 0.125 Izz \\sin{\\left(2 \\operatorname{q_{5}}{\\left(t \\right)} + 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2} - 0.25 Izz \\sin{\\left(2 \\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2} - 1.0 Izz \\sin{\\left(2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} + 0.5 Izz \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} - 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} + 0.5 Izz \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} + 2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{6}}{\\left(t \\right)} + 0.5 f_{1} x_{1} \\sin{\\left(\\beta_{1} - \\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 0.5 f_{1} x_{1} \\sin{\\left(\\beta_{1} + \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 0.5 f_{1} y_{1} \\cos{\\left(\\beta_{1} - \\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 0.5 f_{1} y_{1} \\cos{\\left(\\beta_{1} + \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 0.5 f_{2} x_{2} \\sin{\\left(\\beta_{2} - \\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 0.5 f_{2} x_{2} \\sin{\\left(\\beta_{2} + \\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 0.5 f_{2} y_{2} \\cos{\\left(\\beta_{2} - \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 0.5 f_{2} y_{2} \\cos{\\left(\\beta_{2} + \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 0.5 f_{3} x_{3} \\sin{\\left(\\beta_{3} - \\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 0.5 f_{3} x_{3} \\sin{\\left(\\beta_{3} + \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 0.5 f_{3} y_{3} \\cos{\\left(\\beta_{3} - \\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 0.5 f_{3} y_{3} \\cos{\\left(\\beta_{3} + \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 0.5 f_{4} x_{4} \\sin{\\left(\\beta_{4} - \\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 0.5 f_{4} x_{4} \\sin{\\left(\\beta_{4} + \\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 0.5 f_{4} y_{4} \\cos{\\left(\\beta_{4} - \\operatorname{q_{6}}{\\left(t \\right)} \\right)} + 0.5 f_{4} y_{4} \\cos{\\left(\\beta_{4} + \\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 6.12323399573677 \\cdot 10^{-17} f_{5} x_{5} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 1.0 f_{5} x_{5} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 6.12323399573677 \\cdot 10^{-17} f_{6} x_{6} \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} - 1.0 f_{6} x_{6} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\\\Ixx \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} + Iyy \\left(1 - 2 \\sin^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} + Iyy \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2} - \\frac{Iyy \\sin{\\left(2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)}\\right)^{2}}{2} - Izz \\left(1 - 2 \\sin^{2}{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)}\\right) \\cos{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)} \\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)} - Izz \\sin{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\cos^{2}{\\left(\\operatorname{q_{5}}{\\left(t \\right)} \\right)} \\cos{\\left(\\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{4}}{\\left(t \\right)}\\right)^{2} + \\frac{Izz \\sin{\\left(2 \\operatorname{q_{6}}{\\left(t \\right)} \\right)} \\left(\\frac{d}{d t} \\operatorname{q_{5}}{\\left(t \\right)}\\right)^{2}}{2} + f_{5} y_{5} + f_{6} y_{6}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                                                                             \n",
       "⎢                                                                             \n",
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       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                d         d                              d   \n",
       "⎢- 2.0⋅Ixx⋅sin(q₅(t))⋅cos(q₅(t))⋅──(q₄(t))⋅──(q₅(t)) + 1.0⋅Ixx⋅cos(q₅(t))⋅──(q\n",
       "⎢                                dt        dt                             dt  \n",
       "⎢                                                                             \n",
       "⎢                                                2                            \n",
       "⎢                                     ⎛d        ⎞                   d         \n",
       "⎢                0.5⋅Ixx⋅sin(2⋅q₅(t))⋅⎜──(q₄(t))⎟  - Ixx⋅cos(q₅(t))⋅──(q₄(t))⋅\n",
       "⎢                                     ⎝dt       ⎠                   dt        \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
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       "                                                                      2       \n",
       "      d                                                    ⎛d        ⎞        \n",
       "₅(t))⋅──(q₆(t)) + 1.0⋅Iyy⋅sin(q₅(t))⋅sin(q₆(t))⋅cos(q₆(t))⋅⎜──(q₅(t))⎟  - 2.0⋅\n",
       "      dt                                                   ⎝dt       ⎠        \n",
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       "                                                        2                     \n",
       "d                                            ⎛d        ⎞                      \n",
       "──(q₆(t)) + 0.125⋅Iyy⋅sin(2⋅q₅(t) - 2⋅q₆(t))⋅⎜──(q₄(t))⎟  + 0.125⋅Iyy⋅sin(2⋅q₅\n",
       "dt                                           ⎝dt       ⎠                      \n",
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       "                             2        d         d                             \n",
       "Iyy⋅sin(q₅(t))⋅cos(q₅(t))⋅cos (q₆(t))⋅──(q₄(t))⋅──(q₅(t)) + 2.0⋅Iyy⋅sin(q₅(t))\n",
       "                                      dt        dt                            \n",
       "                                                                              \n",
       "                          2                                    2              \n",
       "               ⎛d        ⎞                          ⎛d        ⎞               \n",
       "(t) + 2⋅q₆(t))⋅⎜──(q₄(t))⎟  - 0.25⋅Iyy⋅sin(2⋅q₅(t))⋅⎜──(q₄(t))⎟  + 1.0⋅Iyy⋅sin\n",
       "               ⎝dt       ⎠                          ⎝dt       ⎠               \n",
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       " -f₁⋅((sin(q₄(t))⋅cos(q₆(t)) - sin(q₅(t))⋅sin(q₆(t))⋅cos(q₄(t)))⋅cos(β₁) - sin\n",
       "                                                                              \n",
       " f₁⋅((sin(q₄(t))⋅sin(q₅(t))⋅sin(q₆(t)) + cos(q₄(t))⋅cos(q₆(t)))⋅cos(β₁) + sin(\n",
       "                                                                              \n",
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       "                                                                              \n",
       "                                                                              \n",
       "            d         d                                 2                   d \n",
       "⋅cos(q₅(t))⋅──(q₄(t))⋅──(q₅(t)) - 2.0⋅Iyy⋅sin(q₆(t))⋅cos (q₅(t))⋅cos(q₆(t))⋅──\n",
       "            dt        dt                                                    dt\n",
       "                                                                              \n",
       "                                                                              \n",
       "          d         d                                        d         d      \n",
       "(2⋅q₆(t))⋅──(q₅(t))⋅──(q₆(t)) - 0.5⋅Iyy⋅cos(q₅(t) - 2⋅q₆(t))⋅──(q₄(t))⋅──(q₆(t\n",
       "          dt        dt                                       dt        dt     \n",
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       "\n",
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       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "(β₁)⋅cos(q₄(t))⋅cos(q₅(t))) - f₂⋅((sin(q₄(t))⋅cos(q₆(t)) - sin(q₅(t))⋅sin(q₆(t\n",
       "                                                                              \n",
       "β₁)⋅sin(q₄(t))⋅cos(q₅(t))) + f₂⋅((sin(q₄(t))⋅sin(q₅(t))⋅sin(q₆(t)) + cos(q₄(t)\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "        d                                 2        d         d                \n",
       "(q₄(t))⋅──(q₆(t)) - 2.0⋅Iyy⋅cos(q₅(t))⋅cos (q₆(t))⋅──(q₅(t))⋅──(q₆(t)) + 1.0⋅I\n",
       "        dt                                         dt        dt               \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                  d         d                                 \n",
       ")) - 0.5⋅Iyy⋅cos(q₅(t) + 2⋅q₆(t))⋅──(q₄(t))⋅──(q₆(t)) - 0.125⋅Izz⋅sin(2⋅q₅(t) \n",
       "                                  dt        dt                                \n",
       "                                                                              \n",
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       "\n",
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       "                                                                              \n",
       "))⋅cos(q₄(t)))⋅cos(β₂) + sin(β₂)⋅cos(q₄(t))⋅cos(q₅(t))) - f₃⋅((sin(q₄(t))⋅cos(\n",
       "                                                                              \n",
       ")⋅cos(q₆(t)))⋅cos(β₂) - sin(β₂)⋅sin(q₄(t))⋅cos(q₅(t))) + f₃⋅((sin(q₄(t))⋅sin(q\n",
       "                                                                              \n",
       "                                        -f₁⋅(sin(β₁)⋅sin(q₅(t)) - sin(q₆(t))⋅c\n",
       "                                                                              \n",
       "                                                                              \n",
       "              d         d                                                ⎛d   \n",
       "yy⋅cos(q₅(t))⋅──(q₅(t))⋅──(q₆(t)) - Izz⋅sin(q₅(t))⋅sin(q₆(t))⋅cos(q₆(t))⋅⎜──(q\n",
       "              dt        dt                                               ⎝dt  \n",
       "                                                                              \n",
       "                      2                                               2       \n",
       "           ⎛d        ⎞                                     ⎛d        ⎞        \n",
       "- 2⋅q₆(t))⋅⎜──(q₄(t))⎟  - 0.125⋅Izz⋅sin(2⋅q₅(t) + 2⋅q₆(t))⋅⎜──(q₄(t))⎟  - 0.25\n",
       "           ⎝dt       ⎠                                     ⎝dt       ⎠        \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                     d        \n",
       "                                                      Ixx⋅cos(q₅(t))⋅──(q₄(t))\n",
       "                                                                     dt       \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "q₆(t)) - sin(q₅(t))⋅sin(q₆(t))⋅cos(q₄(t)))⋅cos(β₃) - sin(β₃)⋅cos(q₄(t))⋅cos(q₅\n",
       "                                                                              \n",
       "₅(t))⋅sin(q₆(t)) + cos(q₄(t))⋅cos(q₆(t)))⋅cos(β₃) + sin(β₃)⋅sin(q₄(t))⋅cos(q₅(\n",
       "                                                                              \n",
       "os(β₁)⋅cos(q₅(t))) + f₂⋅(sin(β₂)⋅sin(q₅(t)) + sin(q₆(t))⋅cos(β₂)⋅cos(q₅(t))) -\n",
       "                                                                              \n",
       "      2                                                                       \n",
       "     ⎞                                     2        d         d               \n",
       "₅(t))⎟  + 2.0⋅Izz⋅sin(q₅(t))⋅cos(q₅(t))⋅cos (q₆(t))⋅──(q₄(t))⋅──(q₅(t)) + 2.0⋅\n",
       "     ⎠                                              dt        dt              \n",
       "                                                                              \n",
       "                             2                                                \n",
       "                  ⎛d        ⎞                     d         d                 \n",
       "⋅Izz⋅sin(2⋅q₅(t))⋅⎜──(q₄(t))⎟  - Izz⋅sin(2⋅q₆(t))⋅──(q₅(t))⋅──(q₆(t)) + 0.5⋅Iz\n",
       "                  ⎝dt       ⎠                     dt        dt                \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       " d               ⎛         2       ⎞            d         d                   \n",
       "⋅──(q₅(t)) + Iyy⋅⎝1 - 2⋅sin (q₆(t))⎠⋅cos(q₅(t))⋅──(q₄(t))⋅──(q₅(t)) + Iyy⋅sin(\n",
       " dt                                             dt        dt                  \n",
       "\n",
       "                                                            d                 \n",
       "                                                            ──(q₁(t))         \n",
       "                                                            dt                \n",
       "                                                                              \n",
       "                                                            d                 \n",
       "                                                            ──(q₂(t))         \n",
       "                                                            dt                \n",
       "                                                                              \n",
       "                                                            d                 \n",
       "                                                            ──(q₃(t))         \n",
       "                                                            dt                \n",
       "                                                                              \n",
       "                                                            d                 \n",
       "                                                            ──(q₄(t))         \n",
       "                                                            dt                \n",
       "                                                                              \n",
       "                                                            d                 \n",
       "                                                            ──(q₅(t))         \n",
       "                                                            dt                \n",
       "                                                                              \n",
       "                                                            d                 \n",
       "                                                            ──(q₆(t))         \n",
       "                                                            dt                \n",
       "                                                                              \n",
       "(t))) - f₄⋅((sin(q₄(t))⋅cos(q₆(t)) - sin(q₅(t))⋅sin(q₆(t))⋅cos(q₄(t)))⋅cos(β₄)\n",
       "                                                                              \n",
       "t))) + f₄⋅((sin(q₄(t))⋅sin(q₅(t))⋅sin(q₆(t)) + cos(q₄(t))⋅cos(q₆(t)))⋅cos(β₄) \n",
       "                                                                              \n",
       " f₃⋅(sin(β₃)⋅sin(q₅(t)) - sin(q₆(t))⋅cos(β₃)⋅cos(q₅(t))) + f₄⋅(sin(β₄)⋅sin(q₅(\n",
       "                                                                              \n",
       "                                                                              \n",
       "                  2                   d         d                             \n",
       "Izz⋅sin(q₆(t))⋅cos (q₅(t))⋅cos(q₆(t))⋅──(q₄(t))⋅──(q₆(t)) + 2.0⋅Izz⋅cos(q₅(t))\n",
       "                                      dt        dt                            \n",
       "                                                                              \n",
       "                                                                              \n",
       "                       d         d                                        d   \n",
       "z⋅cos(q₅(t) - 2⋅q₆(t))⋅──(q₄(t))⋅──(q₆(t)) + 0.5⋅Izz⋅cos(q₅(t) + 2⋅q₆(t))⋅──(q\n",
       "                       dt        dt                                       dt  \n",
       "                                                                              \n",
       "                                                                         2    \n",
       "                                                              ⎛d        ⎞     \n",
       "                                         2   Iyy⋅sin(2⋅q₆(t))⋅⎜──(q₅(t))⎟     \n",
       "          2                   ⎛d        ⎞                     ⎝dt       ⎠     \n",
       "q₆(t))⋅cos (q₅(t))⋅cos(q₆(t))⋅⎜──(q₄(t))⎟  - ───────────────────────────── - I\n",
       "                              ⎝dt       ⎠                  2                  \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       " + sin(β₄)⋅cos(q₄(t))⋅cos(q₅(t))) + f₅⋅(sin(q₄(t))⋅sin(q₆(t)) - 6.123233995736\n",
       "                                                                              \n",
       "- sin(β₄)⋅sin(q₄(t))⋅cos(q₅(t))) + f₅⋅(6.12323399573677e-17⋅sin(q₄(t))⋅sin(q₅(\n",
       "                                                                              \n",
       "t)) + sin(q₆(t))⋅cos(β₄)⋅cos(q₅(t))) + f₅⋅(6.12323399573677e-17⋅sin(q₆(t)) + c\n",
       "                                                                              \n",
       "                                                                              \n",
       "    2        d         d                          d         d                 \n",
       "⋅cos (q₆(t))⋅──(q₅(t))⋅──(q₆(t)) - Izz⋅cos(q₅(t))⋅──(q₅(t))⋅──(q₆(t)) + 1.0⋅f₁\n",
       "             dt        dt                         dt        dt                \n",
       "                                                                              \n",
       "                                                                              \n",
       "      d                                                                       \n",
       "₄(t))⋅──(q₆(t)) + 0.5⋅f₁⋅x₁⋅sin(β₁ - q₆(t)) - 0.5⋅f₁⋅x₁⋅sin(β₁ + q₆(t)) + 0.5⋅\n",
       "      dt                                                                      \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "   ⎛         2       ⎞            d         d                             2   \n",
       "zz⋅⎝1 - 2⋅sin (q₆(t))⎠⋅cos(q₅(t))⋅──(q₄(t))⋅──(q₅(t)) - Izz⋅sin(q₆(t))⋅cos (q₅\n",
       "                                  dt        dt                                \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "77e-17⋅sin(q₄(t))⋅cos(q₆(t)) + 6.12323399573677e-17⋅sin(q₅(t))⋅sin(q₆(t))⋅cos(\n",
       "                                                                              \n",
       "t))⋅sin(q₆(t)) + sin(q₄(t))⋅sin(q₅(t))⋅cos(q₆(t)) - sin(q₆(t))⋅cos(q₄(t)) + 6.\n",
       "                                                                              \n",
       "os(q₆(t)))⋅cos(q₅(t)) + f₆⋅(6.12323399573677e-17⋅sin(q₆(t)) + cos(q₆(t)))⋅cos(\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "⋅x₁⋅cos(β₁)⋅cos(q₅(t))⋅cos(q₆(t)) - f₁⋅y₁⋅sin(β₁)⋅cos(q₅(t))⋅cos(q₆(t)) + 1.0⋅\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "f₁⋅y₁⋅cos(β₁ - q₆(t)) - 0.5⋅f₁⋅y₁⋅cos(β₁ + q₆(t)) + 0.5⋅f₂⋅x₂⋅sin(β₂ - q₆(t)) \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                           2                  \n",
       "                                                ⎛d        ⎞                   \n",
       "                           2   Izz⋅sin(2⋅q₆(t))⋅⎜──(q₅(t))⎟                   \n",
       "                ⎛d        ⎞                     ⎝dt       ⎠                   \n",
       "(t))⋅cos(q₆(t))⋅⎜──(q₄(t))⎟  + ───────────────────────────── + f₅⋅y₅ + f₆⋅y₆  \n",
       "                ⎝dt       ⎠                  2                                \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "q₄(t)) + sin(q₅(t))⋅cos(q₄(t))⋅cos(q₆(t))) + f₆⋅(sin(q₄(t))⋅sin(q₆(t)) - 6.123\n",
       "                                                                              \n",
       "12323399573677e-17⋅cos(q₄(t))⋅cos(q₆(t))) + f₆⋅(6.12323399573677e-17⋅sin(q₄(t)\n",
       "                                                                              \n",
       "q₅(t)) + g⋅m                                                                  \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "f₂⋅x₂⋅cos(β₂)⋅cos(q₅(t))⋅cos(q₆(t)) + 1.0⋅f₂⋅y₂⋅sin(β₂)⋅cos(q₅(t))⋅cos(q₆(t)) \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "- 0.5⋅f₂⋅x₂⋅sin(β₂ + q₆(t)) - 0.5⋅f₂⋅y₂⋅cos(β₂ - q₆(t)) + 0.5⋅f₂⋅y₂⋅cos(β₂ + q\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "23399573677e-17⋅sin(q₄(t))⋅cos(q₆(t)) + 6.12323399573677e-17⋅sin(q₅(t))⋅sin(q₆\n",
       "                                                                              \n",
       ")⋅sin(q₅(t))⋅sin(q₆(t)) + sin(q₄(t))⋅sin(q₅(t))⋅cos(q₆(t)) - sin(q₆(t))⋅cos(q₄\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "+ 1.0⋅f₃⋅x₃⋅cos(β₃)⋅cos(q₅(t))⋅cos(q₆(t)) - f₃⋅y₃⋅sin(β₃)⋅cos(q₅(t))⋅cos(q₆(t)\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "₆(t)) + 0.5⋅f₃⋅x₃⋅sin(β₃ - q₆(t)) - 0.5⋅f₃⋅x₃⋅sin(β₃ + q₆(t)) + 0.5⋅f₃⋅y₃⋅cos(\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "(t))⋅cos(q₄(t)) + sin(q₅(t))⋅cos(q₄(t))⋅cos(q₆(t)))                           \n",
       "                                                                              \n",
       "(t)) + 6.12323399573677e-17⋅cos(q₄(t))⋅cos(q₆(t)))                            \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       ") + 1.0⋅f₄⋅x₄⋅cos(β₄)⋅cos(q₅(t))⋅cos(q₆(t)) + 1.0⋅f₄⋅y₄⋅sin(β₄)⋅cos(q₅(t))⋅cos\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "β₃ - q₆(t)) - 0.5⋅f₃⋅y₃⋅cos(β₃ + q₆(t)) + 0.5⋅f₄⋅x₄⋅sin(β₄ - q₆(t)) - 0.5⋅f₄⋅x\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "(q₆(t)) - f₅⋅x₅⋅sin(q₆(t))⋅cos(q₅(t)) + 6.12323399573677e-17⋅f₅⋅x₅⋅cos(q₅(t))⋅\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "₄⋅sin(β₄ + q₆(t)) - 0.5⋅f₄⋅y₄⋅cos(β₄ - q₆(t)) + 0.5⋅f₄⋅y₄⋅cos(β₄ + q₆(t)) - 6.\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "cos(q₆(t)) - f₅⋅y₅⋅sin(q₅(t)) - f₆⋅x₆⋅sin(q₆(t))⋅cos(q₅(t)) + 6.12323399573677\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "12323399573677e-17⋅f₅⋅x₅⋅sin(q₆(t)) - f₅⋅x₅⋅cos(q₆(t)) - 6.12323399573677e-17⋅\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                   ⎤\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "e-17⋅f₆⋅x₆⋅cos(q₅(t))⋅cos(q₆(t)) - f₆⋅y₆⋅sin(q₅(t))⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "f₆⋅x₆⋅sin(q₆(t)) - f₆⋅x₆⋅cos(q₆(t))                ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎥\n",
       "                                                   ⎦"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.simplify(lm.forcing_full)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "rhs = lm.rhs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Finalmente puede utilizar el modelo del sistema para realizar simulaciones\n",
    "# de dinamica directa utilizando un integrador de ecuaciones diferenciales\n",
    "# de primer orden.\n",
    "\n",
    "# Defina las condiciones iniciales del sistema\n",
    "x0=[0,0,0,0,0,0,0,0,0,0,0,0]\n",
    "# Asigne valores numericos a los parámetros del modelo\n",
    "# rhs.free_symbols (revise las variables libres del modelo)\n",
    "parameters={f1:0,f2:0,f3:0,f4:0,f5:0,f6:0,m:4,Ixx:1064.294e-4,Iyy:1577.872e-4,Izz:951.955e-4,\n",
    "            x1:-0.20,x2:0.20,x3:0.20,x4:-0.20,x5:-0.4,x6:0.4,\n",
    "            y1:0.20,y2:0.20,y3:-0.20,y4:-0.20,y5:0,y6:0,\n",
    "            beta1:np.deg2rad(45),beta2:np.deg2rad(45),beta3:np.deg2rad(45),\n",
    "            beta4:np.deg2rad(45),g:9.8}\n",
    "\n",
    "#Modifique los valores de M1 y M2 para obtener diferentes resultados en\n",
    "# la simulación\n",
    "parameters[f1]=0#-0.1*q1d-0.1*(q1-0.5)\n",
    "parameters[f2]=0#-0.1*q2d-0.1*(q2-0.5)\n",
    "parameters[f3]=0\n",
    "parameters[f4]=0\n",
    "parameters[f5]=0.000001\n",
    "parameters[f6]=0.000001\n",
    "\n",
    "\n",
    "t=np.linspace(0,10,100)\n",
    "# Cree una función numérica del modelo del sistema (i.e xdot=f(x))\n",
    "rhs_fun=lambdify([q1,q2,q3,q4,q5,q6,q1d,q2d,q3d,q4d,q5d,q6d],rhs.subs(parameters))\n",
    "ode_fun=lambda x,t: rhs_fun(x[0],x[1],x[2],x[3],x[4],x[5],x[6],x[7],x[8],x[9],x[10],x[11]).reshape(12)\n",
    "x=odeint(ode_fun,x0,t)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(t,x)\n",
    "plt.legend([q1,q2,q3,q4,q5,q6,q1d,q2d,q3d,q4d,q5d,q6d])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "MovieWriter ffmpeg unavailable; using Pillow instead.\n"
     ]
    }
   ],
   "source": [
    "vis=Visualizer(N,O)\n",
    "vis.add(A,a,shape='sub.stl')\n",
    "vis.add(A,a,frame_scale=100)\n",
    "\n",
    "\n",
    "vis.plot({q1:x0[0],q2:x0[0],q3:x0[0],q4:x0[0],q5:x0[0],q6:x0[0]})\n",
    "vis.fig.savefig('plot1.png')\n",
    "\n",
    "def update(i,data):\n",
    "    vis.plot({q1:data[i,0],q2:data[i,1],q3:data[i,2],q4:data[i,3],q5:data[i,4],q6:data[i,5]})\n",
    "    \n",
    "ani = animation.FuncAnimation(vis.fig, update, x.shape[0], fargs=(x,), interval=10/x.shape[0], blit=False)\n",
    "ani.save('animation1.gif',fps=20)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}