KerMor  0.9
Model order reduction for nonlinear dynamical systems and nonlinear approximation
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plotSingle.m
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1 #include "DynLinTimoshenkoModel.m"
2 namespace models{
3 namespace beam{
4 
5 
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18  */
19 
20 function models.beam.DynLinTimoshenkoModel.plotSingle(double t,colvec u,handle h) {
21 
22 
23 /* nBeams = numel(this.Beams);
24  *
25  * title_string = sprintf('Balkenwerk zur Zeit t = %2.2f (Verschiebungen um Faktor %2.0f vergrößert)', t, this.PlotFactor);
26  * title(title_string, 'FontSize', 12, 'FontWeight', 'bold');
27  *
28  * %% Coloring
29  * col = this.ColorMap;
30  * if isempty(this.cbh)
31  * colormap(col);
32  * this.cbh = colorbar;
33  * xlabel(this.cbh, 'Temperatur', 'FontSize', 12);
34  * end
35  * % Extract temperatures
36  * temps = u(4:4:end);
37  * % For real-time plots: Adopt new heat scale if none set yet
38  * if (max(temps) > this.maxTemp) || (min(temps) < this.minTemp)
39  * this.minTemp = min(temps);
40  * this.maxTemp = max(temps);
41  * caxis([this.minTemp this.maxTemp]);
42  * end
43  * col_index = fix((temps - this.minTemp) / (this.maxTemp - this.minTemp + eps) * (size(col,1)-1)) + 1;
44  *
45  * cla;
46  * hold on;
47  * for i = 1:nBeams
48  * p = this.Beams(i).p(:);
49  * % Ausgangslage
50  * plot3(this.Points(p,1), this.Points(p,2), this.Points(p,3), 'k:' );
51  *
52  * % (End)Indizes der Anfangs- und Endpunkte des Elements im globalen
53  * % Verschiebungsvektor
54  * indices = 4*(this.data.knot_index(p)-1)+1;
55  * % (Verst�rkte) Verschiebung der der Anfangs- u Endpunkte
56  * u_p = this.PlotFactor * [u(indices) u(indices+1) u(indices+2)];
57  * plot3(this.Points(p,1) + u_p(:,1), this.Points(p,2) + u_p(:,2),...
58  * this.Points(p,3) + u_p(:,3), '-+', 'LineWidth', ...
59  * this.BeamLineWidth, 'Color', col(col_index(i),:));
60  * end
61  * hold off; */
62 
63  /* % Plot Options
64  * Vergr��erung der Verschiebungen */
65  plot_options.multiplier= model.PlotFactor;
66  /* Nummer der Figure, in der geplottet wird */
67  plot_options.figure= 11;
68  /* Titel der Colorbar und gleichzeitig zu visualisierende Gr��e
69  * Temperatur, Normalkraft, Querkraft y, Querkraft z, Torsionsmoment,
70  * Biegemoment y, Biegemoment z,
71  * Gesamtquerkraft, Gesamtbiegemoment */
72  plot_options.colorbar= " Normalkraft ";
73  plot_options.axis= " auto ";
74  /* Testszenario
75  * plot_options.axis = [-17 17 -17 2 -2 17]; % Grenzen der Achsen des Plots
76  * Rohrleitungen y
77  * plot_options.axis = [-2 2 -1 11 -4 4]; % Grenzen der Achsen des Plots
78  * Rohrleitungen z
79  * plot_options.axis = [-2 2 -4 4 -1 11]; % Grenzen der Achsen des Plots
80  * Simpel1
81  * plot_options.axis = [-2 17 -1 1 -5 5]; % Grenzen der Achsen des Plots
82  * "Spazierstock"-Testcase (Simpel2)
83  * plot_options.axis = [-17 26 -1 1 -15 10]; % Grenzen der Achsen des Plots */
84 
85  plot_options.centerline= 3; /* Linienst�rke der Mittellinie (0: keine, 1: d�nn, 2: dick mit Endmarkierung) */
86 
87  plot_options.endmarker= 3; /* Linienst�rke der Endmarker */
88 
89  plot_options.crosssection= 0; /* Querschnitte (0: keine, 1: nach Theorie 1. Ordn, 2: Theorie 2. Ordn, sonst: exakt rotiert) */
90 
91  plot_options.ref_config= 1; /* Plotten der Ausgangslage (0: nein, 1: ja) */
92 
93 
94  p = model.Points;
95  video = false;
96  knoten_index = model.data.knot_index;
97 
98  hlp = zeros(7*model.data.num_knots,1);
99  hlp(model.free) = u(1:length(model.free));
100  hlp(model.dir_u) = model.u_dir;
101  u = hlp;
102 
103 /* persistent h; */
104  if nargin == 3 || isempty(h) || ~ishandle(h)
105  h = figure(plot_options.figure);
106  axis equal;
107  axis(plot_options.axis)
108  /* RotMat = viewmtx(37.5, 30);
109  * view(RotMat) */
110 
111  /* Spirale, Rohrleitungen */
112  view(3)
113 
114  /* view(-37.5-video,30)
115  * camva(10)
116  * Portal
117  * view(0,0) */
118  set(h, " Color ", " White ")
119  if (video)
120  set(gcf, " Renderer ", " zbuffer ");
121  end
122 
123  if (strcmp(plot_options.colorbar,) == 0)
124  handle = colorbar;
125  xlabel(handle, plot_options.colorbar, " FontSize ", 12)
126  end
127 
128  hold on;
129  else
130  cla;
131  end
132  title_string = sprintf(" Balkenwerk zur Zeit t = %2.2f (Verschiebungen um Faktor %2.0f vergr��ert) ", t, plot_options.multiplier);
133  title(title_string, " FontSize ", 15, " FontWeight ", " bold ");
134 
135  /* % Ausgangslage */
136  if (plot_options.ref_config)
137  el = model.Elements;
138  for i = 1:length(el)
139  e = el[i];
140  if isa(e," models.beam.StraightBeam ")
141  plot3( p(e.PointsIdx(:),1), p(e.PointsIdx(:),2), p(e.PointsIdx(:),3), " k: ", " LineWidth ", 1 );
142  elseif isa(e," models.beam.CurvedBeam ")
143 /* split = max(fix(split_factor_KR / (0.5*pi/KR(i).angle)), 1); */
144  s = 0 : e.angle/(e.split+1) : e.angle;
145  /* Parametrisierung des Viertelkreises in lokalen Koords */
146  x = e.R * cos(s);
147  y = e.R * sin(s);
148  z = 0*s;
149  /* Umrechnung in globale Koords und Verschiebung um globale Koords des lokalen Ursprungs e.pc */
150  COR = e.T * [x; y; z];
151  plot3( p(e.pc, 1) + COR(1,:), p(e.pc, 2) + COR(2,:), p(e.pc, 3) + COR(3,:), " k: " );
152  else
153  /* for i = 1:num_elem_FH
154  * s = 0 : FH(i).Length/(4*split_factor_FH) : FH(i).Length;
155  * % Parametrisierung des Viertelkreises in lokalen Koords
156  * y = (FH(i).Length/(2*split_factor_FH)) * sin( 2*pi*s / (FH(i).Length/split_factor_FH) );
157  * x = s;
158  * z = 0*s;
159  * % Umrechnung in globale Koords und Verschiebung um globale Koords des
160  * % lokalen Ursprungs e.pc
161  * COR = FH(i).T * [x; y; z];
162  * plot3( p(FH(i).p(1), 1) + COR(1,:), p(FH(i).p(1), 2) + COR(2,:), p(FH(i).p(1), 3) + COR(3,:), 'k:', 'LineWidth', 1 );
163  * end */
164  end
165  end
166  end
167 
168  /* % Berechnung der zu visualisierenden Gr��en
169  * VARIANTE 1: Visualisierung nach Normalkr�ften
170  * -------------------------------------------------------------------------
171  * N = zeros(num_elem_RO + num_elem_KR, 1);
172  * offset = 0;
173  * for i = 1:num_elem_RO
174  *
175  * T_block = RO(i).T;
176  *
177  * u1 = [u(7*knoten_index(RO(i).p(1))-6) u(7*knoten_index(RO(i).p(1))-5) u(7*knoten_index(RO(i).p(1))-4)]';
178  * % t1 = [u(6*knoten_index(e(i,1))-2) u(6*knoten_index(e(i,1))-1) u(6*knoten_index(e(i,1)))]';
179  * u2 = [u(7*knoten_index(RO(i).p(2))-6) u(7*knoten_index(RO(i).p(2))-5) u(7*knoten_index(RO(i).p(2))-4)]';
180  * % t2 = [u(6*knoten_index(e(i,2))-2) u(6*knoten_index(e(i,2))-1) u(6*knoten_index(e(i,2)))]';
181  *
182  * u1_lok = T_block' * u1;
183  * u2_lok = T_block' * u2;
184  * % t1_lok = T_block' * t1;
185  * % t2_lok = T_block' * t2;
186  *
187  * N(i) = (u1_lok(1) - u2_lok(1)) / RO(i).l; */
188 
189  /*
190  * offset = offset + 1;
191  * end
192  *
193  * for i = 1:num_elem_KR
194  *
195  * indices = 7*knoten_index(KR(i).p(:));
196  * % Verschiebung der der Anfangs- u Endpunkte
197  * u_elem = [u(indices-6) u(indices-5) u(indices-4) u(indices-3) u(indices-2) u(indices-1)];
198  *
199  * T_block_0 = KR(i).T * KR(i).Fren(0);
200  * T_block_L = KR(i).T * KR(i).Fren(KR(i).angle);
201  *
202  * u0_lok = T_block_0' * u_elem(1,1:3)';
203  * t0_lok = T_block_0' * u_elem(1,4:6)';
204  * uL_lok = T_block_L' * u_elem(2,1:3)';
205  * tL_lok = T_block_L' * u_elem(2,4:6)';
206  *
207  * x = [u0_lok; t0_lok; uL_lok; tL_lok];
208  *
209  * [Ns, B] = circle_shape_functions(KR(i).R, KR(i).R * KR(i).angle, 0);
210  *
211  * Q = B(7:9,:)*x;
212  *
213  * N(offset + i) = Q(1);
214  *
215  * end
216  *
217  * N_min = min(N);
218  * N_max = max(N); */
219 
220 
221  /* VARIANTE 2: Visualisierung nach Temperatur
222  * ------------------------------------------------------------------------- */
223  el = model.Elements;
224  N = zeros(length(el));
225  idx = [];
226  for i = 1:length(el)
227  e = el[i];
228  if ~isa(e," models.beam.Truss ")
229  idx(end+1) = i;/* #ok */
230 
231  N(i) = .5*sum(u(7*knoten_index(e.PointsIdx(:))));
232  end
233  end
234  /* Reduce to actually assigned temperatures (excluding trusses)
235  * N(i) entspricht Farbe f�r this.Elements{idx(i)} */
236  N = N(idx);
237 
238  N_min = 0;
239  N_max = 2e6;
240 
241  /* % Colormaps und Farbindexing
242  * col = colormap('hot');
243  * Eigene Colormap erstellen (num_col Farben)
244  * blau -> gr�n -> rot
245  * num_col = 128;
246  * dc = [0:2/num_col:1]';
247  * col = [0*dc dc 1-dc; dc 1-dc 0*dc];
248  * blau -> gr�n -> gelb -> rot */
249  num_col = 128;
250  dc = [0:3/num_col:1]^t;
251  col = [0*dc dc 1-dc; dc 0*dc+1 0*dc; 0*dc+1 1-dc 0*dc];
252  colormap(col);
253  caxis([N_min N_max]);
254 
255  /* Den einzelnen Werten von N den richtigen Index in der Colormap zuweisen */
256  if ( (N_max - N_min) > 1e-5 )
257  col_index = fix( (N - N_min) / (N_max - N_min) * (size(col,1)-1)) + 1;
258  else
259  col_index = 0*N + fix(size(col,1)/2);
260  end
261 
262  col_index(col_index > num_col) = 128;
263  col_index(col_index < 1) = 1;
264 
265  val_min = +1e20;
266  val_max = -1e20;
267 
268  /* % Plotten */
269  offset = 0;
270  for i = 1:length(el)
271  e = el[i];
272  if isa(e," models.beam.StraightBeam ")
273  /* (End)Indizes der Anfangs- und Endpunkte des Elements im globalen
274  * Verschiebungsvektor */
275  indices = 7*knoten_index(e.PointsIdx(:));
276  /* (Verst�rkte) Verschiebung der der Anfangs- u Endpunkte
277  * u_p = plot_options.multiplier * [u(indices-6) u(indices-5) u(indices-4)]; */
278 
279  /* plot3( p(e.p(:),1) + u_p(:,1), p(e.p(:),2) + u_p(:,2), p(e.p(:),3) + u_p(:,3), '-+', 'LineWidth', 3, 'Color', col(col_index(i),:) ); */
280  offset = offset + 1;
281 
282  u1_lok = [e.T" * u([indices(1)-6:indices(1)-4]); e.T " * u([indices(1)-3:indices(1)-1])];
283  u2_lok = [e.T" * u([indices(2)-6:indices(2)-4]); e.T " * u([indices(2)-3:indices(2)-1])];
284 
285  /* Ableitungen der Basisfunktionen */
286  N_prime_1 = e.beam_shape_functions_derivative(0);
287  N_prime_2 = e.beam_shape_functions_derivative(e.Length);
288  /* Ableitungen der Variablen berechnen */
289  u1_prime_lok = N_prime_1 * [u1_lok; u2_lok];
290  u2_prime_lok = N_prime_2 * [u1_lok; u2_lok];
291 
292  if ( strcmpi(plot_options.colorbar, " Temperatur ") )
293  /* Temperatur */
294  val1 = u(7*knoten_index(e.p(1)));
295  val2 = u(7*knoten_index(e.p(2)));
296  elseif ( strcmpi(plot_options.colorbar, " Normalkraft ") )
297  /* Normalenkraft */
298  val1 = e.c(13) * e.Length * u1_prime_lok(1);
299  val2 = e.c(13) * e.Length * u2_prime_lok(1);
300  elseif ( strcmpi(plot_options.colorbar, " Querkraft y ") )
301  /* Querkraft y */
302  val1 = e.c(3) / e.Length * (u1_prime_lok(2) - u1_lok(6));
303  val2 = e.c(3) / e.Length * (u2_prime_lok(2) - u2_lok(6));
304  elseif ( strcmpi(plot_options.colorbar, " Querkraft z ") )
305  /* Querkraft z */
306  val1 = e.c(3) / e.Length * (u1_prime_lok(3) - u1_lok(5));
307  val2 = e.c(3) / e.Length * (u2_prime_lok(3) - u2_lok(5));
308  elseif ( strcmpi(plot_options.colorbar, " Gesamtquerkraft ") )
309  /* Gesamtquerkraft */
310  val1 = e.c(3) / e.Length * sqrt((u1_prime_lok(2) - u1_lok(6))^2 + (u1_prime_lok(3) - u1_lok(5))^2);
311  val2 = e.c(3) / e.Length * sqrt((u2_prime_lok(2) - u2_lok(6))^2 + (u2_prime_lok(3) - u2_lok(5))^2);
312  elseif ( strcmpi(plot_options.colorbar, " Torsionsmoment ") )
313  /* Torsionsmoment */
314  val1 = e.c(14) * e.Length * abs(u1_prime_lok(4));
315  val2 = e.c(14) * e.Length * abs(u2_prime_lok(4));
316  elseif ( strcmpi(plot_options.colorbar, " Biegemoment y ") )
317  /* Biegemoment y */
318  val1 = e.c(1) * u1_prime_lok(5);
319  val2 = e.c(1) * u2_prime_lok(5);
320  elseif ( strcmpi(plot_options.colorbar, " Biegemoment z ") )
321  /* Biegemoment z */
322  val1 = e.c(1) * u1_prime_lok(6);
323  val2 = e.c(1) * u2_prime_lok(6);
324  elseif ( strcmpi(plot_options.colorbar, " Gesamtbiegemoment ") )
325  /* Gesamtbiegemoment */
326  val1 = e.c(1) * sqrt(u1_prime_lok(5)^2 + u1_prime_lok(6)^2);
327  val2 = e.c(1) * sqrt(u2_prime_lok(5)^2 + u2_prime_lok(6)^2);
328  else
329  /* Keine Farbe */
330  val1 = N_min;
331  val2 = N_min;
332  end
333 
334  if (val1 > val_max)
335  val_max = val1;
336  end
337  if (val2 > val_max)
338  val_max = val2;
339  end
340  if (val1 < val_min)
341  val_min = val1;
342  end
343  if (val2 < val_min)
344  val_min = val2;
345  end
346 
347  /* Den farbgebenden Werten col1 u col2 aufgrund der Grenzen N_min/max Farbindex zuweisen */
348  cols = fix( ([val1 val2] - N_min) / (N_max - N_min) * (size(col,1)-1)) + 1;
349  cols(cols > num_col) = num_col;
350  cols(cols < 1) = 1;
351  /* this.plot_beam(e.split, e.T, e.c, p(e.PointsIdx(1),:), p(e.PointsIdx(2),:), plot_options.multiplier*u1_lok, plot_options.multiplier*u2_lok, cols(1), cols(2), plot_options) */
352  e.plot(p, plot_options.multiplier*u1_lok, plot_options.multiplier*u2_lok, cols(1), cols(2), plot_options)
353 
354  elseif isa(e," models.beam.CurvedBeam ")
355  /* (End)Indizes der Anfangs- und Endpunkte des Elements im globalen
356  * Verschiebungsvektor */
357  indices = 7*knoten_index(e.PointsIdx(:));
358 
359  /* Verschiebung der der Anfangs- u Endpunkte */
360  u_elem = [u(indices-6) u(indices-5) u(indices-4) u(indices-3) u(indices-2) u(indices-1)];
361 
362 /* split = max(fix(split_factor_KR / (0.5*pi/e.angle)), 1);
363  * split = e.split;
364  * s = ( 0 : (e.angle/split) : e.angle );
365  *
366  * x = e.R * cos(s);
367  * y = e.R * sin(s);
368  * z = 0*s;
369  * COR = e.T * [x; y; z]; */
370 
371  u1_lok = e.T_block1" * u_elem(1,1:3) ";
372  t1_lok = e.T_block1" * u_elem(1,4:6) ";
373  u2_lok = e.T_block2" * u_elem(2,1:3) ";
374  t2_lok = e.T_block2" * u_elem(2,4:6) ";
375  u1 = [u1_lok; t1_lok];
376  u2 = [u2_lok; t2_lok];
377 
378  /* d/ds(u) - theta x e_1 (Querkr�fte ohne Stoffkonstanten) */
379  Q_temp = e.B3*[u1; u2];
380  /* d/ds(theta) (Momente ohne Stoffkonstanten) */
381  M_temp = e.B4*[u1; u2];
382 
383  if ( strcmpi(plot_options.colorbar, " Temperatur ") )
384  /* Temperatur */
385  val1 = u(7*knoten_index(e.PointsIdx(1)));
386  val2 = u(7*knoten_index(e.PointsIdx(2)));
387  /* Schnittgr��en �ber Element konstant! */
388  elseif ( strcmpi(plot_options.colorbar, " Normalkraft ") )
389  /* Normalenkraft */
390  val1 = e.c(3) * Q_temp(1);
391  val2 = val1;
392  elseif ( strcmpi(plot_options.colorbar, " Querkraft y ") )
393  /* Querkraft y */
394  val1 = e.c(4) * Q_temp(2);
395  val2 = val1;
396  elseif ( strcmpi(plot_options.colorbar, " Querkraft z ") )
397  /* Querkraft z */
398  val1 = e.c(4) * Q_temp(3);
399  val2 = val1;
400  elseif ( strcmpi(plot_options.colorbar, " Gesamtquerkraft ") )
401  /* Gesamtquerkraft */
402  val1 = e.c(4) * sqrt(Q_temp(2)^2 + Q_temp(3)^2);
403  val2 = val1;
404  elseif ( strcmpi(plot_options.colorbar, " Torsionsmoment ") )
405  /* Torsionsmoment */
406  val1 = e.c(2) * abs(M_temp(1));
407  val2 = val1;
408  elseif ( strcmpi(plot_options.colorbar, " Biegemoment y ") )
409  /* Biegemoment y */
410  val1 = e.c(1) * M_temp(2);
411  val2 = val1;
412  elseif ( strcmpi(plot_options.colorbar, " Biegemoment z ") )
413  /* Biegemoment z */
414  val1 = e.c(1) * M_temp(3);
415  val2 = val1;
416  elseif ( strcmpi(plot_options.colorbar, " Gesamtbiegemoment ") )
417  /* Gesamtbiegemoment */
418  val1 = e.c(1) * sqrt(M_temp(2)^2 + M_temp(3)^2);
419  val2 = val1;
420  else
421  /* Keine Farbe */
422  val1 = N_min;
423  val2 = val1;
424  end
425 
426  if (val1 > val_max)
427  val_max = val1;
428  end
429  if (val2 > val_max)
430  val_max = val2;
431  end
432  if (val1 < val_min)
433  val_min = val1;
434  end
435  if (val2 < val_min)
436  val_min = val2;
437  end
438 
439  cols = fix( ([val1 val2] - N_min) / (N_max - N_min) * (size(col,1)-1)) + 1;
440  cols(cols > num_col) = num_col;
441  cols(cols < 1) = 1;
442  u1 = plot_options.multiplier * u1;
443  u2 = plot_options.multiplier * u2;
444 
445  e.plot(p, u1, u2, cols(1), cols(2), plot_options);
446 
447 /* x = [u0_lok; t0_lok; uL_lok; tL_lok];
448  * x_lok = zeros(6, length(s));
449  * for j = 1:length(s)
450  * Ns = circle_shape_functions(e.R, e.R*s(j), e.B);
451  * x_lok(:,j) = Ns*x;
452  * end
453  *
454  * u_lok = x_lok(1:3,:);
455  * u_p = 0*u_lok;
456  * u_p(:,1) = plot_factor * u_elem(1,1:3)';
457  * u_p(:,length(s)) = plot_factor * u_elem(2,1:3)';
458  * for k = 2:length(s)-1
459  * u_p(:,k) = plot_factor * e.T * e.Fren(s(k)) * u_lok(:,k);
460  * end
461  * plot3( p(e.pc, 1) + COR(1,:) + u_p(1,:), p(e.pc, 2) + COR(2,:) + u_p(2,:), p(e.pc, 3) + COR(3,:) + u_p(3,:), 'LineWidth', 3, 'Color', col(col_index(offset + i),:) );
462  * plot3( p(e.PointsIdx(:),1) + u_p(1,[1 length(s)])', p(e.PointsIdx(:),2) + + u_p(2,[1 length(s)])', p(e.PointsIdx(:),3) + u_p(3,[1 length(s)])', '+', 'LineWidth', 3, 'Color', col(col_index(offset + i),:) );
463  * % plot3( p(e.pc, 1) + COR(1,:) + u_p(1,:), p(e.pc, 2) + COR(2,:) + u_p(2,:), p(e.pc, 3) + COR(3,:) + u_p(3,:), 'LineWidth', 3); */
464 
465  /* % Plot of Truss elements */
466  else
467  /* Verschiebungsvektor */
468  indices = 7*knoten_index(e.PointsIdx(:));
469 
470  /* Verschiebung der der Anfangs- u Endpunkte */
471  u_elem = [u(indices-6) u(indices-5) u(indices-4)];
472 
473  if (i==5)
474  plot3( p(e.PointsIdx(:), 1) + plot_options.multiplier *u_elem(:,1), p(e.PointsIdx(:), 2) + plot_options.multiplier *u_elem(:,2), p(e.PointsIdx(:), 3) + plot_options.multiplier *u_elem(:,3), " k ", " LineWidth ", 3 );
475  continue;
476  end
477 
478  e.plot(p, u_elem, plot_options);
479  end
480  end
481 
482  /* Geschwindigkeitsvektoren plotten
483  * for i = 1:length(knoten_index)
484  * if (knoten_index(i))
485  * quiver3(p(i,1)+plot_factor*u(7*knoten_index(i)-6), p(i,2)+plot_factor*u(7*knoten_index(i)-5), p(i,3)+plot_factor*u(7*knoten_index(i)-4), v(7*knoten_index(i)-6), v(7*knoten_index(i)-5), v(7*knoten_index(i)-4), 'Color', [0 0 1])
486  * end
487  * end */
488 
489  /* camup([-1 0 1])
490  * campos([0 6 0])
491  * camtarget([0 0 0]) */
492 
493  /* val_min
494  *val_max */
495 
496  /* Frame f�r Video speichern und anh�ngen */
497  if (video)
498  frame = getframe(gcf);
499  else
500  frame = 0;
501  end
502 end
503 }
524 };
525 };
models.beam.DynLinTimoshenkoModel.plotSingle
function plotSingle(double t,colvec u,handle h)
plot_single: Plots a single beam configuration for given time and field data.
Definition: plotSingle.m:20
handle
Matlab's base handle class (documentation generation substitute)
Definition: class_substitutes.c:91
colvec
A matlab column vector.
DynLinTimoshenkoModel.m
t
* t
Definition: Gordon66SarcoForceLength.m:116