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alTmp.009
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degrees off
autoz on
Newtonian N
Bodies DiskA, DiskB
bodies FakeA, FakeB
points ahat,bhat
points fakeahat, fakebhat
motionvariables' u', fakeu{6}'
variables e{4}',posa{3}',posb{3}',ke,pe,cahat{3}',cbhat{3}', q{3}'
variables u{6}
variables aforce{3},bforce{3}
variables fakee{4}'
constants l,rad,a,qq{3}, gamma
l = sqrt(2) * rad * gamma
a = pi/2
mass diska = m
mass diskb = m
inertia diska,m*rad*rad/4,m*rad*rad/4,m*rad*rad/2
inertia diskb,m*rad*rad/4,m*rad*rad/4,m*rad*rad/2
mass fakea = m
mass fakeb = m
inertia fakea,m*rad*rad/4,m*rad*rad/4,m*rad*rad/2
inertia fakeb,m*rad*rad/4,m*rad*rad/4,m*rad*rad/2
dircos(N,DiskA,Euler,e1,e2,e3,e4)
dircos(DiskA,DiskB,body123,pi/2,0,0)
dircos(N,fakeA,Euler,fakee1,fakee2,fakee3,fakee4)
dircos(fakeA,fakeB,body123,pi/2,0,0)
%gamma is l/sqrt(2)/r
p_diskao_ahat> = rad * unitvec(dot(diska3>,n3>)*diska3>-n3>)
p_diskbo_bhat> = rad * unitvec(dot(diskb3>,n3>)*diskb3>-n3>)
p_diskao_diskbo> = -l * diska1>
p_fakeao_fakeahat> = rad * unitvec(dot(fakea3>,n3>)*fakea3>-n3>)
p_fakebo_fakebhat> = rad * unitvec(dot(fakeb3>,n3>)*fakeb3>-n3>)
p_fakeao_fakebo> = -l * fakea1>
w_diska_n> = u * unitvec(p_ahat_bhat>)
w_diskb_diska> = 0>
w_fakea_n> = fakeu1 * fakea1> + fakeu2 * fakea2> + fakeu3 * fakea3>
w_fakeb_fakea> = 0>
kindiffs(N,DiskA,Euler,e1,e2,e3,e4)
kindiffs(N,FakeA,Euler,fakee1,fakee2,fakee3,fakee4)
v_ahat_n> = 0>
v_diskao_n> = v_ahat_n> + cross(w_diska_n>,p_ahat_diskao>)
v_diskbo_n> = v_diskao_n> + cross(w_diska_n>,p_diskao_diskbo>)
v_bhat_n> = 0>
v_fakeao_n> = fakeu4 * n1> + fakeu5 * n2> + fakeu6 * n3>
v_fakebo_n> = v_fakeao_n> + cross(w_fakea_n>,p_fakeao_fakebo>)
v_fakeahat_n> = v_fakeao_n> + cross(w_fakea_n>,p_fakeao_fakeahat>)
v_fakebhat_n> = v_fakebo_n> + cross(w_fakea_n>,p_fakebo_fakebhat>)
u1 = dot(w_diska_n>,diska1>)
u2 = dot(w_diska_n>,diska2>)
u3 = dot(w_diska_n>,diska3>)
u4 = dot(v_diskao_n>, n1>)
u5 = dot(v_diskao_n>, n2>)
u6 = dot(v_diskao_n>, n3>)
gravity(-9.81*n3>)
force_fakeahat> = aforce1 * n1> + aforce2 * n2> + aforce3 * n3>
force_fakebhat> = bforce1 * n1> + bforce2 * n2> + bforce3 * n3>
%autoz on
zee_not=[aforce1,aforce2,aforce3,bforce1,bforce2,bforce3]
zero = fr() + frstar()
newzero = zero[1]
solve(newzero,u')
%'
forcezero = [zero[2],zero[3],zero[4],zero[5],zero[6],zero[7]]
%explicit(forcezero)
forces = [aforce1,aforce2,aforce3,bforce1,bforce2,bforce3]
%forcezero = replace(forcezero,fakeu1=u1,fakeu2=u2,fakeu3=u3,fakeu4=u4, &
% fakeu5=u5,fakeu6=u6,fakee1=e1,fakee2=e2,fakee3=e3,fakee4=e4, &
% fakeu1'=Dt(u1),fakeu2'=Dt(u2),fakeu3'=Dt(u3),fakeu4'=Dt(u4), &
% fakeu5'=Dt(u5),fakeu6'=Dt(u6))
solve(forcezero,forces)
fakee1 = e1
fakee2 = e2
fakee3 = e3
fakee4 = e4
fakee1' = e1'
fakee2' = e2'
fakee3' = e3'
fakee4' = e4'
fakeu1 = u1
fakeu2 = u2
fakeu3 = u3
fakeu4 = u4
fakeu5 = u5
fakeu6 = u6
fakeu1' = Dt(u1)
fakeu2' = Dt(u2)
fakeu3' = Dt(u3)
fakeu4' = Dt(u4)
fakeu5' = Dt(u5)
fakeu6' = Dt(u6)
posa1' = dot(v_diskao_n>,n1>)
posa2' = dot(v_diskao_n>,n2>)
posa3' = dot(v_diskao_n>,n3>)
posb1' = dot(v_diskbo_n>,n1>)
posb2' = dot(v_diskbo_n>,n2>)
posb3' = dot(v_diskbo_n>,n3>)
cahat1' = dot((v_diskao_n>+cross(w_diska_n>-u3*diska3>,p_diskao_ahat>)) ,n1>)
cahat2' = dot((v_diskao_n>+cross(w_diska_n>-u3*diska3>,p_diskao_ahat>)) ,n2>)
cahat3' = 0
cbhat1' = dot((v_diskbo_n>+cross(w_diskb_n>-dot(w_diskb_n>,diskb3>)*diskb3>,p_diskbo_bhat>)) ,n1>)
cbhat2' = dot((v_diskbo_n>+cross(w_diskb_n>-dot(w_diskb_n>,diskb3>)*diskb3>,p_diskbo_bhat>)) ,n2>)
cbhat3' = 0
ke = m/2*dot(v_diskao_n>,v_diskao_n>)+m/2*dot(v_diskbo_n>,v_diskbo_n>) + &
dot(w_diska_n>,dot(I_diska_diskao>>,w_diska_n>))/2 + &
dot(w_diskb_n>,dot(I_diskb_diskbo>>,w_diskb_n>))/2
pe = 9.81*m*posa3 + 9.81*m*posb3
qq1 = pi/4
qq2 = 0
qq3 = 0
%qq1 = 0
%qq2 = asin(rad/(rad+l))
%qq3 = 0
q1' = u1
q2' = u2
q3' = u3
%'
input rad = .1, m = 2
input gamma = 1
input e4 = cos(qq1/2)*cos(qq2/2)*cos(qq3/2)+sin(qq1/2)*sin(qq2/2)*sin(qq3/2)
input e1 = sin(qq1/2)*cos(qq2/2)*cos(qq3/2)-cos(qq1/2)*sin(qq2/2)*sin(qq3/2)
input e2 = cos(qq1/2)*sin(qq2/2)*cos(qq3/2)+sin(qq1/2)*cos(qq2/2)*sin(qq3/2)
input e3 = cos(qq1/2)*cos(qq2/2)*sin(qq3/2)-sin(qq1/2)*sin(qq2/2)*cos(qq3/2)
input u = 1
inputVecto = [dot(p_ahat_diskao>,n1>), dot(p_ahat_diskao>,n2>), &
dot(p_ahat_diskao>,n3>), &
dot(p_diskao_diskbo>,n1>) + dot(p_ahat_diskao>,n1>), &
dot(p_diskao_diskbo>,n2>) + dot(p_ahat_diskao>,n2>), &
dot(p_diskao_diskbo>,n3>) + dot(p_ahat_diskao>,n3>), &
0, 0, 0, dot(p_ahat_bhat>,n1>), dot(p_ahat_bhat>,n2>), 0, &
dot(v_diskao_n>,n1>),dot(v_diskao_n>,n2>), &
dot(v_diskao_n>,n3>),u1,u2,u3]
explicit(inputVecto)
inputVector = replace(inputVecto,e1=input(e1),e2=input(e2),e3=input(e3), &
e4=input(e4),u=input(u),a=input(a), &
gamma=input(gamma),rad=input(rad))
input posa1 = inputVector[1], posa2 = inputVector[2], posa3 = inputVector[3]
input posb1 = inputVector[4], posb2 = inputVector[5], posb3 = inputVector[6]
input cahat1 = 0, cahat2 = 0, cahat3 = 0
input cbhat1 = inputVector[10], cbhat2 = inputVector[11], cbhat3 = 0
output t,ke,pe,ke+pe,e1,e2,e3,e4,u, &
cahat1,cahat2,cahat3,cbhat1,cbhat2,cbhat3, &
u1,u2,u3,u4,u5,u6, q1,q2,q3, &
aforce1,aforce2,aforce3,bforce1,bforce2,bforce3
%code dynamics() TwinDisksConstraintForcesExtra.m
%exit
explicit(u4)
explicit(aforce1)