-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathTwinDisksConstraintForces.m~
472 lines (432 loc) · 24.7 KB
/
TwinDisksConstraintForces.m~
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
function TwinDisksConstraintForces
SolveOrdinaryDifferentialEquations
% File TwinDisksConstraintForces.m created by Autolev 4.1 on Mon Sep 27 21:24:43 2010
function VAR = ReadUserInput
global gamma m rad;
global cahat1 cahat2 cahat3 cbhat1 cbhat2 cbhat3 e1 e2 e3 e4 posa1 posa2 posa3 posb1 posb2 posb3 q1 q2 q3 u;
global l aforce1 aforce2 aforce3 aforcespeed1 aforcespeed2 aforcespeed3 bforce1 bforce2 bforce3 bforcespeed1 bforcespeed2 bforcespeed3 ke pe u3 cahat1p cahat2p cahat3p cbhat1p cbhat2p cbhat3p e1p e2p e3p e4p posa1p posa2p posa3p posb1p posb2p posb3p q1p q2p q3p up;
global DEGtoRAD RADtoDEG z;
global TINITIAL TFINAL INTEGSTP PRINTINT ABSERR RELERR;
%-------------------------------+--------------------------+-------------------+-----------------
% Quantity | Value | Units | Description
%-------------------------------|--------------------------|-------------------|-----------------
gamma = 1; % UNITS Constant
m = 2; % UNITS Constant
rad = .1; % UNITS Constant
cahat1 = 0; % UNITS Initial Value
cahat2 = 0; % UNITS Initial Value
cahat3 = 0; % UNITS Initial Value
cbhat1 = -0.1414214; % UNITS Initial Value
cbhat2 = 0.1414213562373095; % UNITS Initial Value
cbhat3 = 0; % UNITS Initial Value
e1 = 0.3826834323650898; % UNITS Initial Value
e2 = 0; % UNITS Initial Value
e3 = 0; % UNITS Initial Value
e4 = 0.9238795325112867; % UNITS Initial Value
posa1 = 0; % UNITS Initial Value
posa2 = 0.07071067811865475; % UNITS Initial Value
posa3 = 0.07071067811865477; % UNITS Initial Value
posb1 = -0.1414214; % UNITS Initial Value
posb2 = 0.07071067811865475; % UNITS Initial Value
posb3 = 0.07071067811865477; % UNITS Initial Value
q1 = 0.0; % UNITS Initial Value
q2 = 0.0; % UNITS Initial Value
q3 = 0.0; % UNITS Initial Value
u = 5.041; % UNITS Initial Value
TINITIAL = 0.0; % UNITS Initial Time
TFINAL = 1.0; % UNITS Final Time
INTEGSTP = 0.01; % UNITS Integration Step
PRINTINT = 1; % Positive Integer Print-Integer
ABSERR = 1.0E-08; % Absolute Error
RELERR = 1.0E-07 ; % Relative Error
%-------------------------------+--------------------------+-------------------+-----------------
% Unit conversions
Pi = 3.141592653589793;
DEGtoRAD = Pi/180.0;
RADtoDEG = 180.0/Pi;
% Reserve space and initialize matrices
z = zeros(171,1);
% Evaluate constants
aforcespeed1 = 0;
aforcespeed2 = 0;
aforcespeed3 = 0;
bforcespeed1 = 0;
bforcespeed2 = 0;
bforcespeed3 = 0;
z(1) = m*rad^2;
cahat3p = 0;
cbhat3p = 0;
l = 1.414213562373095*gamma*rad;
z(24) = l^2;
% Set the initial values of the states
VAR(1) = cahat1;
VAR(2) = cahat2;
VAR(3) = cahat3;
VAR(4) = cbhat1;
VAR(5) = cbhat2;
VAR(6) = cbhat3;
VAR(7) = e1;
VAR(8) = e2;
VAR(9) = e3;
VAR(10) = e4;
VAR(11) = posa1;
VAR(12) = posa2;
VAR(13) = posa3;
VAR(14) = posb1;
VAR(15) = posb2;
VAR(16) = posb3;
VAR(17) = q1;
VAR(18) = q2;
VAR(19) = q3;
VAR(20) = u;
%===========================================================================
function OpenOutputFilesAndWriteHeadings
FileIdentifier = fopen('TwinDisksConstraintForces.1', 'wt'); if( FileIdentifier == -1 ) error('Error: unable to open file TwinDisksConstraintForces.1'); end
fprintf( 1, '%% t ke pe ke+pe dot(v_bhat_n>, dot(v_bhat_n>, e1 e2 e3 e4 u cahat1 cahat2 cahat3 cbhat1 cbhat2 cbhat3 dot(w_diska_n> dot(w_diska_n> dot(w_diska_n> q1 q2 q3 aforce1 aforce2 aforce3 bforce1 bforce2 bforce3\n' );
fprintf( 1, '%% (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS)\n\n' );
fprintf(FileIdentifier, '%% FILE: TwinDisksConstraintForces.1\n%%\n' );
fprintf(FileIdentifier, '%% t ke pe ke+pe dot(v_bhat_n>, dot(v_bhat_n>, e1 e2 e3 e4 u cahat1 cahat2 cahat3 cbhat1 cbhat2 cbhat3 dot(w_diska_n> dot(w_diska_n> dot(w_diska_n> q1 q2 q3 aforce1 aforce2 aforce3 bforce1 bforce2 bforce3\n' );
fprintf(FileIdentifier, '%% (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS) (UNITS)\n\n' );
%===========================================================================
% Main driver loop for numerical integration of differential equations
%===========================================================================
function SolveOrdinaryDifferentialEquations
global gamma m rad;
global cahat1 cahat2 cahat3 cbhat1 cbhat2 cbhat3 e1 e2 e3 e4 posa1 posa2 posa3 posb1 posb2 posb3 q1 q2 q3 u;
global l aforce1 aforce2 aforce3 aforcespeed1 aforcespeed2 aforcespeed3 bforce1 bforce2 bforce3 bforcespeed1 bforcespeed2 bforcespeed3 ke pe u3 cahat1p cahat2p cahat3p cbhat1p cbhat2p cbhat3p e1p e2p e3p e4p posa1p posa2p posa3p posb1p posb2p posb3p q1p q2p q3p up;
global DEGtoRAD RADtoDEG z;
global TINITIAL TFINAL INTEGSTP PRINTINT ABSERR RELERR;
OpenOutputFilesAndWriteHeadings
VAR = ReadUserInput;
OdeMatlabOptions = odeset( 'RelTol',RELERR, 'AbsTol',ABSERR, 'MaxStep',INTEGSTP );
T = TINITIAL;
PrintCounter = 0;
mdlDerivatives(T,VAR,0);
while 1,
if( TFINAL>=TINITIAL & T+0.01*INTEGSTP>=TFINAL ) PrintCounter = -1; end
if( TFINAL<=TINITIAL & T+0.01*INTEGSTP<=TFINAL ) PrintCounter = -1; end
if( PrintCounter <= 0.01 ),
mdlOutputs(T,VAR,0);
if( PrintCounter == -1 ) break; end
PrintCounter = PRINTINT;
end
[TimeOdeArray,VarOdeArray] = ode45( @mdlDerivatives, [T T+INTEGSTP], VAR, OdeMatlabOptions, 0 );
TimeAtEndOfArray = TimeOdeArray( length(TimeOdeArray) );
if( abs(TimeAtEndOfArray - (T+INTEGSTP) ) >= abs(0.001*INTEGSTP) ) warning('numerical integration failed'); break; end
T = TimeAtEndOfArray;
VAR = VarOdeArray( length(TimeOdeArray), : );
PrintCounter = PrintCounter - 1;
end
mdlTerminate(T,VAR,0);
data = load('TwinDisksConstraintForces.1');
figure(1),plot(data(:,1),data(:,24),data(:,1),data(:,25),data(:,1),data(:,26),data(:,1),data(:,27),data(:,1),data(:,28),data(:,1),data(:,29))
legend('a1','a2','a3','b1','b2','b3')
figure(2),plot(data(:,1),data(:,18))
figure(3),plot(data(:,1),data(:,2))
%===========================================================================
% mdlDerivatives: Calculates and returns the derivatives of the continuous states
%===========================================================================
function sys = mdlDerivatives(T,VAR,u)
global gamma m rad;
global cahat1 cahat2 cahat3 cbhat1 cbhat2 cbhat3 e1 e2 e3 e4 posa1 posa2 posa3 posb1 posb2 posb3 q1 q2 q3 u;
global l aforce1 aforce2 aforce3 aforcespeed1 aforcespeed2 aforcespeed3 bforce1 bforce2 bforce3 bforcespeed1 bforcespeed2 bforcespeed3 ke pe u3 cahat1p cahat2p cahat3p cbhat1p cbhat2p cbhat3p e1p e2p e3p e4p posa1p posa2p posa3p posb1p posb2p posb3p q1p q2p q3p up;
global DEGtoRAD RADtoDEG z;
global TINITIAL TFINAL INTEGSTP PRINTINT ABSERR RELERR;
% Update variables after integration step
cahat1 = VAR(1);
cahat2 = VAR(2);
cahat3 = VAR(3);
cbhat1 = VAR(4);
cbhat2 = VAR(5);
cbhat3 = VAR(6);
e1 = VAR(7);
e2 = VAR(8);
e3 = VAR(9);
e4 = VAR(10);
posa1 = VAR(11);
posa2 = VAR(12);
posa3 = VAR(13);
posb1 = VAR(14);
posb2 = VAR(15);
posb3 = VAR(16);
q1 = VAR(17);
q2 = VAR(18);
q3 = VAR(19);
u = VAR(20);
z(8) = 2*e1*e3 - 2*e2*e4;
z(9) = 2*e1*e4 + 2*e2*e3;
z(17) = 1 - z(9)^2;
z(18) = z(17)^0.5;
z(19) = z(9)/z(18);
z(21) = rad*z(19);
z(10) = 1 - 2*e1^2 - 2*e2^2;
z(11) = 1 - z(10)^2;
z(12) = z(11)^0.5;
z(14) = 1/z(12);
z(16) = rad*z(14);
z(20) = 1/z(18);
z(22) = rad*z(20);
z(23) = z(16) - z(22);
z(13) = z(10)/z(12);
z(15) = rad*z(13);
z(25) = z(24) + z(15)^2 + z(21)^2 + z(23)^2 + 2*z(9)*z(21)*z(23) - 2*l*z(8)*z(23) - 2*z(10)*z(15)*z(23);
z(26) = z(25)^0.5;
z(28) = z(23)/z(26);
z(27) = z(15)/z(26);
z(33) = z(10)*z(28) - z(27);
z(42) = z(21)*z(33);
z(29) = l/z(26);
z(31) = z(8)*z(28) - z(29);
z(39) = z(15)*z(31);
z(30) = z(21)/z(26);
z(32) = z(30) + z(9)*z(28);
z(38) = z(15)*z(32);
z(43) = z(21)*z(31);
z(46) = m*(z(8)*z(42)+z(9)*z(39)-z(8)*z(38)-z(10)*z(43));
z(51) = z(32)*u;
z(52) = z(33)*u;
z(75) = z(1)*z(52);
z(74) = z(1)*z(51);
z(84) = 0.5*z(51)*z(75) - 0.25*z(52)*z(74);
z(87) = 0.25*z(51)*z(75) - 0.5*z(52)*z(74);
z(50) = z(31)*u;
z(73) = z(1)*z(50);
z(83) = 0.25*z(52)*z(73) - 0.5*z(50)*z(75);
z(82) = 0.25*z(50)*z(74) - 0.25*z(51)*z(73);
z(85) = 0.5*z(50)*z(74) - 0.25*z(51)*z(73);
z(34) = e2*z(33) + e4*z(31) - e3*z(32);
z(35) = e3*z(31) + e4*z(32) - e1*z(33);
z(54) = (e1*z(34)+e2*z(35))*u;
z(55) = z(10)*z(54)/z(11)^0.5;
z(60) = (z(10)*z(55)+z(12)*z(54))/z(12)^2;
z(56) = rad*z(55)/z(12)^2;
z(37) = e1*z(31) + e2*z(32) + e3*z(33);
z(36) = e1*z(32) + e4*z(33) - e2*z(31);
z(57) = (e1*z(37)-e2*z(36)-e3*z(35)-e4*z(34))*u;
z(58) = z(9)*z(57)/z(17)^0.5;
z(59) = rad*z(58)/z(18)^2;
z(53) = (e1*z(36)+e2*z(37)+e3*z(34)-e4*z(35))*u;
z(61) = (z(9)*z(58)+z(18)*z(57))/z(18)^2;
z(62) = 4*z(15)*z(23)*z(54) + 4*rad*z(10)*z(23)*z(60) + 2*l*z(8)*(2*z(56)-z(59)) + 2*z(10)*z(15)*(2*z(56)-z(59)) - 4*rad*z(15)*z(60) - 2*l*z(23)*z(53) - 2*rad*z(21)*z(61) - 2*z(21)*z(23)*z(57) - 2*rad*z(9)*z(23)*z(61) - 2*z(23)*(2*z(56)-z(59)) - 2*z(9)*z(21)*(2*z(56)-z(59));
z(64) = l*z(62)/(z(25)^0.5*z(26)^2);
z(63) = (z(23)*z(62)/z(25)^0.5+2*z(26)*(2*z(56)-z(59)))/z(26)^2;
z(65) = 0.5*z(64) + z(28)*z(53) - 0.5*z(8)*z(63);
z(66) = u*z(65);
z(77) = z(1)*z(66);
z(67) = (2*rad*z(26)*z(61)+z(21)*z(62)/z(25)^0.5)/z(26)^2;
z(68) = -0.5*z(67) - z(28)*z(57) - 0.5*z(9)*z(63);
z(69) = u*z(68);
z(79) = z(1)*z(69);
z(70) = (4*rad*z(26)*z(60)+z(15)*z(62)/z(25)^0.5)/z(26)^2;
z(71) = 0.5*z(70) - 2*z(28)*z(54) - 0.5*z(10)*z(63);
z(72) = u*z(71);
z(81) = z(1)*z(72);
z(94) = z(15)*z(65) - 2*rad*z(31)*z(60);
z(95) = u*z(94);
z(88) = aforcespeed1 - z(38)*u;
z(108) = z(95) + z(52)*z(88) - aforcespeed3*z(50);
z(5) = 2*e1*e2 + 2*e3*e4;
z(6) = 1 - 2*e1^2 - 2*e3^2;
z(7) = 2*e2*e3 - 2*e1*e4;
z(40) = z(16)*(z(5)*z(31)+z(6)*z(32)+z(7)*z(33));
z(96) = (e3*z(37)-e1*z(35)-e2*z(34)-e4*z(36))*u;
z(97) = (e1*z(34)+e3*z(36))*u;
z(98) = (e1*z(37)+e2*z(36)+e3*z(35)-e4*z(34))*u;
z(99) = -2*(z(5)*z(31)+z(6)*z(32)+z(7)*z(33))*z(56) - z(16)*(z(31)*z(96)+2*z(32)*z(97)-z(5)*z(65)-z(6)*z(68)-z(7)*z(71)-z(33)*z(98));
z(100) = u*z(99);
z(2) = 1 - 2*e2^2 - 2*e3^2;
z(3) = 2*e1*e2 - 2*e3*e4;
z(4) = 2*e1*e3 + 2*e2*e4;
z(41) = z(16)*(z(2)*z(31)+z(3)*z(32)+z(4)*z(33));
z(102) = (e1*z(35)+e2*z(34)+e3*z(37)-e4*z(36))*u;
z(101) = (e2*z(35)+e3*z(36))*u;
z(103) = (e2*z(37)-e1*z(36)-e3*z(34)-e4*z(35))*u;
z(104) = z(16)*(z(2)*z(65)+z(3)*z(68)+z(4)*z(71)+z(32)*z(102)-2*z(31)*z(101)-z(33)*z(103)) - 2*(z(2)*z(31)+z(3)*z(32)+z(4)*z(33))*z(56);
z(105) = u*z(104);
z(92) = z(15)*z(68) - 2*rad*z(32)*z(60);
z(93) = u*z(92);
z(89) = aforcespeed2 + z(39)*u;
z(106) = aforcespeed3*z(51) - z(93) - z(52)*z(89);
z(107) = z(50)*z(89) - z(51)*z(88);
z(113) = z(21)*z(71) - rad*z(33)*z(61);
z(114) = u*z(113);
z(110) = bforcespeed2 - z(43)*u;
z(121) = z(114) + bforcespeed3*z(52) + z(51)*z(110);
z(44) = z(22)*(z(5)*z(31)+z(6)*z(32)+z(7)*z(33));
z(117) = -(z(5)*z(31)+z(6)*z(32)+z(7)*z(33))*z(59) - z(22)*(z(31)*z(96)+2*z(32)*z(97)-z(5)*z(65)-z(6)*z(68)-z(7)*z(71)-z(33)*z(98));
z(118) = u*z(117);
z(45) = z(22)*(z(2)*z(31)+z(3)*z(32)+z(4)*z(33));
z(119) = z(22)*(z(2)*z(65)+z(3)*z(68)+z(4)*z(71)+z(32)*z(102)-2*z(31)*z(101)-z(33)*z(103)) - (z(2)*z(31)+z(3)*z(32)+z(4)*z(33))*z(59);
z(120) = u*z(119);
z(115) = z(21)*z(65) - rad*z(31)*z(61);
z(116) = u*z(115);
z(109) = bforcespeed1 + z(42)*u;
z(122) = -z(116) - bforcespeed3*z(50) - z(51)*z(109);
z(123) = z(50)*z(110) - z(52)*z(109);
z(86) = 0.25*z(50)*z(75) - 0.25*z(52)*z(73);
z(125) = z(31)*z(84) + z(31)*z(87) + z(32)*z(83) + z(33)*z(82) + z(33)*z(85) + 0.5*z(31)*z(77) + 0.75*z(32)*z(79) + 0.75*z(33)*z(81) + m*(z(39)*z(108)+z(40)*z(100)+z(41)*z(105)+z(2)*z(40)*z(106)+z(3)*z(39)*z(100)+z(3)*z(40)*z(108)+z(4)*z(40)*z(107)+z(5)*z(38)*z(105)-z(38)*z(106)-z(2)*z(38)*z(100)-z(5)*z(41)*z(106)-z(6)*z(39)*z(105)-z(6)*z(41)*z(108)-z(7)*z(41)*z(107)) + m*(z(42)*z(121)+z(44)*z(118)+z(45)*z(120)+z(2)*z(42)*z(118)+z(2)*z(44)*z(121)+z(4)*z(44)*z(122)+z(6)*z(45)*z(123)+z(7)*z(43)*z(120)-z(43)*z(122)-z(3)*z(44)*z(123)-z(4)*z(43)*z(118)-z(5)*z(42)*z(120)-z(5)*z(45)*z(121)-z(7)*z(45)*z(122)) - z(32)*z(86);
z(138) = -9.810000000000001*z(46) - z(125);
z(76) = z(1)*z(31);
z(78) = z(1)*z(32);
z(80) = z(1)*z(33);
z(124) = 0.5*z(31)*z(76) + 0.75*z(32)*z(78) + 0.75*z(33)*z(80) + m*(z(38)^2+z(39)^2+z(40)^2+z(41)^2+2*z(3)*z(39)*z(40)+2*z(5)*z(38)*z(41)-2*z(2)*z(38)*z(40)-2*z(6)*z(39)*z(41)) - m*(2*z(4)*z(43)*z(44)+2*z(5)*z(42)*z(45)-z(42)^2-z(43)^2-z(44)^2-z(45)^2-2*z(2)*z(42)*z(44)-2*z(7)*z(43)*z(45));
z(171) = z(138)/z(124);
up = z(171);
e1p = 0.5*z(34)*u;
e2p = 0.5*z(35)*u;
e3p = 0.5*z(36)*u;
e4p = -0.5*z(37)*u;
posa1p = z(4)*aforcespeed3 + z(40)*u + z(3)*(aforcespeed2+z(39)*u) + z(2)*(aforcespeed1-z(38)*u);
posa2p = z(7)*aforcespeed3 + z(6)*(aforcespeed2+z(39)*u) + z(5)*(aforcespeed1-z(38)*u) - z(41)*u;
posa3p = z(10)*aforcespeed3 + z(9)*(aforcespeed2+z(39)*u) + z(8)*(aforcespeed1-z(38)*u);
posb1p = z(44)*u + z(2)*(bforcespeed1+z(42)*u) + z(4)*(bforcespeed2-z(43)*u) - z(3)*bforcespeed3;
posb2p = z(5)*(bforcespeed1+z(42)*u) + z(7)*(bforcespeed2-z(43)*u) - z(6)*bforcespeed3 - z(45)*u;
posb3p = z(8)*(bforcespeed1+z(42)*u) + z(10)*(bforcespeed2-z(43)*u) - z(9)*bforcespeed3;
u3 = z(33)*u;
cahat1p = z(4)*aforcespeed3 + z(40)*u + z(7)*z(16)*(u3-z(33)*u) + z(3)*(aforcespeed2+z(39)*u-z(15)*z(31)*u) - z(5)*z(16)*z(31)*u - z(6)*z(16)*z(32)*u - z(2)*(z(38)*u-aforcespeed1-z(15)*z(32)*u);
cahat2p = z(7)*aforcespeed3 + z(2)*z(16)*z(31)*u + z(3)*z(16)*z(32)*u + z(6)*(aforcespeed2+z(39)*u-z(15)*z(31)*u) - z(41)*u - z(4)*z(16)*(u3-z(33)*u) - z(5)*(z(38)*u-aforcespeed1-z(15)*z(32)*u);
cbhat1p = z(2)*(bforcespeed1+z(42)*u-z(21)*z(33)*u) + (z(44)-z(5)*z(22)*z(31)-z(7)*z(22)*z(33))*u - z(3)*bforcespeed3 - z(4)*(z(43)*u-bforcespeed2-z(21)*z(31)*u);
cbhat2p = z(5)*(bforcespeed1+z(42)*u-z(21)*z(33)*u) - z(6)*bforcespeed3 - z(7)*(z(43)*u-bforcespeed2-z(21)*z(31)*u) - (z(45)-z(2)*z(22)*z(31)-z(4)*z(22)*z(33))*u;
q1p = z(31)*u;
q2p = z(32)*u;
q3p = z(33)*u;
% Update derivative array prior to integration step
VARp(1) = cahat1p;
VARp(2) = cahat2p;
VARp(3) = cahat3p;
VARp(4) = cbhat1p;
VARp(5) = cbhat2p;
VARp(6) = cbhat3p;
VARp(7) = e1p;
VARp(8) = e2p;
VARp(9) = e3p;
VARp(10) = e4p;
VARp(11) = posa1p;
VARp(12) = posa2p;
VARp(13) = posa3p;
VARp(14) = posb1p;
VARp(15) = posb2p;
VARp(16) = posb3p;
VARp(17) = q1p;
VARp(18) = q2p;
VARp(19) = q3p;
VARp(20) = up;
sys = VARp';
%===========================================================================
% mdlOutputs: Calculates and return the outputs
%===========================================================================
function Output = mdlOutputs(T,VAR,u)
global gamma m rad;
global cahat1 cahat2 cahat3 cbhat1 cbhat2 cbhat3 e1 e2 e3 e4 posa1 posa2 posa3 posb1 posb2 posb3 q1 q2 q3 u;
global l aforce1 aforce2 aforce3 aforcespeed1 aforcespeed2 aforcespeed3 bforce1 bforce2 bforce3 bforcespeed1 bforcespeed2 bforcespeed3 ke pe u3 cahat1p cahat2p cahat3p cbhat1p cbhat2p cbhat3p e1p e2p e3p e4p posa1p posa2p posa3p posb1p posb2p posb3p q1p q2p q3p up;
global DEGtoRAD RADtoDEG z;
global TINITIAL TFINAL INTEGSTP PRINTINT ABSERR RELERR;
% Evaluate output quantities
ke = 0.375*z(1)*z(33)^2*u^2 + 0.25*z(1)*(z(31)^2+1.5*z(32)^2)*u^2 + 0.5*m*(aforcespeed3^2+z(40)^2*u^2+z(41)^2*u^2+(aforcespeed2+z(39)*u)^2+2*z(4)*z(40)*aforcespeed3*u+(aforcespeed1-z(38)*u)^2+2*z(3)*z(40)*u*(aforcespeed2+z(39)*u)+2*z(2)*z(40)*u*(aforcespeed1-z(38)*u)-2*z(7)*z(41)*aforcespeed3*u-2*z(6)*z(41)*u*(aforcespeed2+z(39)*u)-2*z(5)*z(41)*u*(aforcespeed1-z(38)*u)) + 0.5*m*(bforcespeed3^2+z(44)^2*u^2+z(45)^2*u^2+(bforcespeed1+z(42)*u)^2+2*z(6)*z(45)*bforcespeed3*u+(bforcespeed2-z(43)*u)^2+2*z(2)*z(44)*u*(bforcespeed1+z(42)*u)+2*z(4)*z(44)*u*(bforcespeed2-z(43)*u)-2*z(3)*z(44)*bforcespeed3*u-2*z(5)*z(45)*u*(bforcespeed1+z(42)*u)-2*z(7)*z(45)*u*(bforcespeed2-z(43)*u));
pe = 9.810000000000001*m*(posa3+posb3);
z(147) = z(5)*z(9) - z(6)*z(8);
z(49) = m*z(10);
z(131) = m*(z(107)+z(4)*z(100)-z(7)*z(105));
z(141) = -9.810000000000001*z(49) - z(131);
z(149) = z(6)*z(10) - z(7)*z(9);
z(47) = m*z(8);
z(127) = m*(z(106)+z(2)*z(100)-z(5)*z(105));
z(139) = -9.810000000000001*z(47) - z(127);
z(152) = z(5)*z(10) - z(7)*z(8);
z(48) = m*z(9);
z(129) = m*(z(108)+z(3)*z(100)-z(6)*z(105));
z(140) = -9.810000000000001*z(48) - z(129);
z(145) = z(2)*z(6) - z(3)*z(5);
z(146) = z(2)*z(9) - z(3)*z(8);
z(148) = z(4)*z(147) + z(10)*z(145) - z(7)*z(146);
z(156) = (z(147)*z(141)+z(149)*z(139)-z(152)*z(140))/z(148);
z(128) = m*(z(39)+z(3)*z(40)-z(6)*z(41));
z(126) = m*(z(2)*z(40)-z(38)-z(5)*z(41));
z(130) = m*(z(4)*z(40)-z(7)*z(41));
z(155) = (z(128)*z(152)-z(126)*z(149)-z(130)*z(147))/z(148);
aforce1 = -z(156) - z(155)*up;
z(150) = z(3)*z(10) - z(4)*z(9);
z(153) = z(2)*z(10) - z(4)*z(8);
z(158) = (z(146)*z(141)+z(150)*z(139)-z(153)*z(140))/z(148);
z(157) = (z(128)*z(153)-z(126)*z(150)-z(130)*z(146))/z(148);
aforce2 = z(158) + z(157)*up;
z(151) = z(3)*z(7) - z(4)*z(6);
z(154) = z(2)*z(7) - z(4)*z(5);
z(160) = (z(145)*z(141)+z(151)*z(139)-z(154)*z(140))/z(148);
z(159) = (z(128)*z(154)-z(126)*z(151)-z(130)*z(145))/z(148);
aforce3 = -z(160) - z(159)*up;
z(132) = m*(z(42)+z(2)*z(44)-z(5)*z(45));
z(134) = m*(z(4)*z(44)-z(43)-z(7)*z(45));
z(162) = z(6)*z(8) - z(5)*z(9);
z(136) = m*(z(3)*z(44)-z(6)*z(45));
z(161) = z(6)*z(153) - z(3)*z(152) - z(9)*z(154);
z(165) = (z(132)*z(149)-z(134)*z(162)-z(136)*z(152))/z(161);
z(133) = m*(z(121)+z(2)*z(118)-z(5)*z(120));
z(142) = -9.810000000000001*z(47) - z(133);
z(137) = m*(z(3)*z(118)-z(123)-z(6)*z(120));
z(144) = 9.810000000000001*z(48) + z(137);
z(135) = m*(z(122)+z(4)*z(118)-z(7)*z(120));
z(143) = -9.810000000000001*z(49) - z(135);
z(166) = (z(149)*z(142)+z(152)*z(144)-z(162)*z(143))/z(161);
bforce1 = z(165)*up - z(166);
z(163) = z(3)*z(8) - z(2)*z(9);
z(168) = (z(150)*z(142)+z(153)*z(144)-z(163)*z(143))/z(161);
z(167) = (z(132)*z(150)-z(134)*z(163)-z(136)*z(153))/z(161);
bforce2 = z(168) - z(167)*up;
z(164) = z(3)*z(5) - z(2)*z(6);
z(169) = (z(132)*z(151)-z(134)*z(164)-z(136)*z(154))/z(161);
z(170) = (z(151)*z(142)+z(154)*z(144)-z(164)*z(143))/z(161);
bforce3 = z(169)*up - z(170);
Output(1)=T; Output(2)=ke; Output(3)=pe; Output(4)=ke+pe; Output(5)=((l*z(2)+z(4)*z(15)-z(3)*z(21))*bforcespeed1*z(5)+(z(6)*z(21)-l*z(5)-z(7)*z(15))*bforcespeed1*z(2)+(l*z(2)+z(4)*z(15)-z(3)*z(21))*bforcespeed2*z(7)+(z(6)*z(21)-l*z(5)-z(7)*z(15))*bforcespeed2*z(4)-(l*z(2)+z(4)*z(15)-z(3)*z(21))*bforcespeed3*z(6)-(z(6)*z(21)-l*z(5)-z(7)*z(15))*bforcespeed3*z(3)); Output(6)=(bforcespeed1*z(8)+bforcespeed2*z(10)-bforcespeed3*z(9)); Output(7)=e1; Output(8)=e2; Output(9)=e3; Output(10)=e4; Output(11)=u; Output(12)=cahat1; Output(13)=cahat2; Output(14)=cahat3; Output(15)=cbhat1; Output(16)=cbhat2; Output(17)=cbhat3; Output(18)=(z(31)*u); Output(19)=(z(32)*u); Output(20)=(z(33)*u); Output(21)=q1; Output(22)=q2; Output(23)=q3; Output(24)=aforce1; Output(25)=aforce2; Output(26)=aforce3; Output(27)=bforce1; Output(28)=bforce2; Output(29)=bforce3;
FileIdentifier = fopen('all');
WriteOutput( 1, Output(1:29) );
WriteOutput( FileIdentifier(1), Output(1:29) );
%===========================================================================
function WriteOutput( fileIdentifier, Output )
numberOfOutputQuantities = length( Output );
if numberOfOutputQuantities > 0,
for i=1:numberOfOutputQuantities,
fprintf( fileIdentifier, ' %- 14.6E', Output(i) );
end
fprintf( fileIdentifier, '\n' );
end
%===========================================================================
% mdlTerminate: Perform end of simulation tasks and set sys=[]
%===========================================================================
function sys = mdlTerminate(T,VAR,u)
FileIdentifier = fopen('all');
fclose( FileIdentifier(1) );
fprintf( 1, '\n Output is in the file TwinDisksConstraintForces.1\n' );
fprintf( 1, '\n To load and plot columns 1 and 2 with a solid line and columns 1 and 3 with a dashed line, enter:\n' );
fprintf( 1, ' someName = load( ''TwinDisksConstraintForces.1'' );\n' );
fprintf( 1, ' plot( someName(:,1), someName(:,2), ''-'', someName(:,1), someName(:,3), ''--'' )\n\n' );
sys = [];
%===========================================================================
% Sfunction: System/Simulink function from standard template
%===========================================================================
function [sys,x0,str,ts] = Sfunction(t,x,u,flag)
switch flag,
case 0, [sys,x0,str,ts] = mdlInitializeSizes; % Initialization of sys, initial state x0, state ordering string str, and sample times ts
case 1, sys = mdlDerivatives(t,x,u); % Calculate the derivatives of continuous states and store them in sys
case 2, sys = mdlUpdate(t,x,u); % Update discrete states x(n+1) in sys
case 3, sys = mdlOutputs(t,x,u); % Calculate outputs in sys
case 4, sys = mdlGetTimeOfNextVarHit(t,x,u); % Return next sample time for variable-step in sys
case 9, sys = mdlTerminate(t,x,u); % Perform end of simulation tasks and set sys=[]
otherwise error(['Unhandled flag = ',num2str(flag)]);
end
%===========================================================================
% mdlInitializeSizes: Return the sizes, initial state VAR, and sample times ts
%===========================================================================
function [sys,VAR,stateOrderingStrings,timeSampling] = mdlInitializeSizes
sizes = simsizes; % Call simsizes to create a sizes structure
sizes.NumContStates = 20; % sys(1) is the number of continuous states
sizes.NumDiscStates = 0; % sys(2) is the number of discrete states
sizes.NumOutputs = 29; % sys(3) is the number of outputs
sizes.NumInputs = 0; % sys(4) is the number of inputs
sizes.DirFeedthrough = 1; % sys(6) is 1, and allows for the output to be a function of the input
sizes.NumSampleTimes = 1; % sys(7) is the number of samples times (the number of rows in ts)
sys = simsizes(sizes); % Convert it to a sizes array
stateOrderingStrings = [];
timeSampling = [0 0]; % m-by-2 matrix containing the sample times
OpenOutputFilesAndWriteHeadings
VAR = ReadUserInput