Particles chain with V-model interaction
Материал из Department of Theoretical and Applied Mechanics
The virtual laboratory > Particles chain with V-model interaction
Содержание
The short description of V - model
V-model is used for the description of loose solid bodies, for example rocks, ceramics, concrete, nanocomposites and agglomerates.
The model is described by the following formulas:
Interaction force:
Moments:
Where , , and - various coefficients which are characteristics of system.
Description of realization of a chain
In the program three various boundary conditions which can are realized chosen as the user:
- The free chain
- Chain with clenched left edge
- Chain with clenched edges
Also the user in the first two cases can move an extreme right particle, and in the third case can move the central right particle.
An opportunity to set starting conditions for all chains is provided:
- To set an amount of twist of particles from each other.
- To set the relative displacement of particles along OX axis
- To set the relative displacement of particles along OY axis
Also there is an opportunity to set stiffness factors of system on various movements. Which are bound to coefficients from the formulas stated above for V - model.
- Rigidity on stretching compression:
- Rigidity on shift:
- Rigidity on a bend:
- Rigidity on torsion:
Realization of a chain
The program given below realizes a chain of particles, interaction between which is V - model.
Download V-model.
The text of the program in the JavaScript (developer Lapin Ruslan):
File "V-model.js"
1 function MainParticle(canvas) {
2 // Presets
3 var context = canvas.getContext("2d"); // on context drawing takes place
4
5 // Specifying constants
6 const Pi = 3.1415926; // "Pi"
7 const m0 = 1; // weight scale
8 const T0 = 1; // time scale (the period of oscillation of the original system )
9 const a0 = 1; // distance scale ( ball diameter)
10 const g0 = a0 / T0 / T0; // accelerating the scale (acceleration , in which for T0 be completed distance a0)
11 const k0 = 2 * Pi / T0; // frequency scale
12 //const C0 = m0 * k0 * k0; // hardness scale
13 const C0 = 1;
14 const B0 = 2 * m0 * k0; // viscosity scale
15
16 // *** Setting physical parameters ***
17
18 const Ny = 5; // the number of balls is placed vertically in a window ( sets the size of the ball relative to the window size )
19 const Nx = 5;
20 const m = 1 * m0; // weight
21 const Cwall = 10 * C0; // wall stiffness
22 //const B = 0.01 * B0; // viscosity of the environment
23 const B = 0;
24 const B1 = 0.03 * B0; // viscosity on the walls
25 //const B1 = 0;
26 //var mg = 0.25 * m * g0; // gravity
27 const r = 0.5 * a0; // the radius of the particles in the calculated coordinates
28 var stiff = 1 * C0; // "Rigidity" of a spring
29
30 var vx0 = 0 * a0/T0;
31 var vy0 = 0 * a0/T0;
32 //Text_vx0.value = vx0;
33
34 // *** System settings ***
35 var c = 1;// rigidity
36 var n = 10;// the amount of particles
37 var c_a = 100//1;//longitudinal
38 var c_d = 100//c_a*1;//shear
39 var c_b = 0.1//c_a;//bending
40 var c_t = 1;//torsional
41 var J = 1;
42 var m_0 = 1.5;
43 var f = 0 ;//option or free body or fixed edge
44 var ugol = 0;
45 var sm_x = 0;
46 var sm_y = 0;
47
48
49 // *** Setting the parameters of computing ***
50
51 const fps = 50; // frames per second - the number of frames per second ( kachectvo display )50
52 const spf = 10;//5; // steps per frame - the number of integration steps between frames ( calculation speed)
53 const dt = 1 * T0 / fps; // the integration step
54
55 // Setting constants for drawing
56 const scale =100* canvas.height / Ny / a0; // a scaling factor for the transition from design to screen coordinates
57
58 var w = canvas.width / scale; // width of the window in the calculated coordinates
59 var h = canvas.height / scale; // window height in calculated coordinates
60 var k1v; var k2v; var k3v; var k4v; var k1x; var k2x; var k3x; var k4x;
61 var T1;var T2; var T1_; var T2_;
62 var rectH = 50;
63 var rectW = 50;
64 var diag = (rectH/scale)*Math.cos(45*Math.PI/180);
65 var koeff = 1;
66 var B_1 =c_a;
67 var B_2 = c_d*diag*diag;
68 var B_4 = c_t;
69 var B_3 = c_b - B_2/4 - B_4/2;
70
71 // ------------------------------- Implementation of the program ------------------------------------------
72 // Addition of a sphere
73 balls=[]//the massif containing particles
74 j=1;
75 for (i = 0;i<n/2;i++)
76 {
77 var b = [];
78 var b1 = [];
79 var time = 1;
80 b.fi_x = 0*j; //corner with an axis OX
81 b.omega=0;// angular velocity
82 var dx = diag*Math.cos(b.fi_x*Math.PI/180);//shift for drawing.
83 j=j*(-1);
84 b.x = (w / 2)-diag*(2*i+1)*1.0; b.y = h / 2.0; // calculated coordinates of a sphere
85 b.Fx=0;b.Fy=0;
86 b.x_ = b.x; b.y_ = b.y;
87 b.fx = 0; b.fy = 0; // force operating on a spher
88 b.vx = vx0; b.vy = vy0; // initial velocity
89 b1.fi_x = 0*j; //corner with an axis OX
90 b1.omega=0;
91 b1.Fx=0;b1.Fy=0;
92 b1.x = (w / 2)+diag*(2*i+1)*1.0; b1.y = h / 2 ; // calculated coordinates of a sphere
93 b1.x_ = b.x; b1.y_ = b.y;
94 b1.fx = 0; b1.fy = 0; // force operating on a sphere
95 b1.vx = vx0; b1.vy = vy0; // initial velocity
96 balls[n/2-(i+1)]=b;//[2*i]
97 balls[n/2+(i)] = b1;//[2*i+1]
98
99 }
100 // Basis cycle of the program
101 setInterval(control, 1500 / fps); // function control is caused with the period determined by the second parameter
102
103 // ---------------------------------------------------------------------------------------------------------------------
104 // --------------------------------- Definition of all functions -----------------------------------
105 // ---------------------------------------------------------------------------------------------------------------------
106
107 // the trial function caused in the program
108 function control()
109 {
110 physics(); // we do spf of steps an integration
111 draw(); // we draw a particle
112 }
113 //=======================new task of a reference state
114 function rebild()//new task of a reference state
115 {
116 time = 1;
117 balls=[]
118 j=1;
119 ugol = 0;
120 sm_x = 0;
121 sm_y = 0;
122 for (i = 0;i<n/2;i++)
123 {
124 var b = [];
125 var b1 = [];
126 var time = 1;
127 b.fi_x = 0*j; //corner with an axis ОХ
128 b.omega=0;//angular velocity
129 var dx = diag*Math.cos(b.fi_x*Math.PI/180);//shift for drawing.
130 j=j*(-1);
131 b.x = (w / 2)-diag*(2*i+1)*1.0; b.y = h / 2.0; // calculated coordinates of a sphere
132 b.Fx=0;b.Fy=0;
133 b.x_ = b.x; b.y_ = b.y;
134 b.fx = 0; b.fy = 0; // force operating on a sphere
135 b.vx = vx0; b.vy = vy0; // initial velocity
136 b1.fi_x = 0*j; //corner with an axis ОХ
137 b1.omega=0;
138 b1.Fx=0;b1.Fy=0;
139 b1.x = (w / 2)+diag*(2*i+1)*1.0; b1.y = h / 2 ; // calculated coordinates of a sphere
140 b1.x_ = b.x; b1.y_ = b.y;
141 b1.fx = 0; b1.fy = 0; // force operating on a sphere
142 b1.vx = vx0; b1.vy = vy0; // initial velocity
143 balls[n/2-(i+1)]=b;//[2*i]
144 balls[n/2+(i)] = b1;//[2*i+1]
145
146 }
147 context.clearRect(0, 0, w * scale, h * scale);
148 }
149 //=======================The choice like task======================
150
151 radio_pic_1.onchange = function() {f = 0;rebild();};//the free body
152 radio_pic_2.onchange = function() {f = 1;rebild();};//the fixed edge
153 radio_pic_3.onchange = function() {f = 2;rebild();};//the fixed edges
154
155 // Reaction to change of value in a checkbox
156
157 this.new_start = function()
158 {
159 rebild();
160 }
161 this.set_c_a = function(input)
162 {
163 c_a = Number(input);
164 B_1 =c_a;
165 time = 1;
166 for (i = 0;i<n/2;i++)
167 {
168 var b = [];
169 var b1 = [];
170 var time = 1;
171 b.fi_x = ugol*j; //corner with an axis ОХ
172 b.omega=0;//angular velocity
173 var dx = diag*Math.cos(b.fi_x*Math.PI/180);//shift for drawing.
174 j=j*(-1);
175 b.x = (w / 2)-diag*(2*i+1)*(1.0+sm_x/100); b.y = h / (2.00+sm_y/100); // calculated coordinates of a sphere
176 b.Fx=0;b.Fy=0;
177 b.x_ = b.x; b.y_ = b.y;
178 b.fx = 0; b.fy = 0; // force operating on a sphere
179 b.vx = vx0; b.vy = vy0; // initial velocity
180 b1.fi_x = ugol*j; //corner with an axis ОХ
181 b1.omega=0;
182 b1.Fx=0;b1.Fy=0;
183 b1.x = (w / 2)+diag*(2*i+1)*(1.0+sm_x/100); b1.y = h / (2.00-sm_y/100) ; // force operating on a sphere
184 b1.x_ = b.x; b1.y_ = b.y;
185 b1.fx = 0; b1.fy = 0; // force operating on a sphere
186 b1.vx = vx0; b1.vy = vy0; // initial velocity
187 balls[n/2-(i+1)]=b;//[2*i]
188 balls[n/2+(i)] = b1;//[2*i+1]
189
190 }
191 context.clearRect(0, 0, w * scale, h * scale);
192 }
193 this.set_c_b = function(input)
194 {
195 c_b = Number(input);
196 B_3 = c_b - B_2/4 - B_4/2;
197 time = 1;
198 for (i = 0;i<n/2;i++)
199 {
200 var b = [];
201 var b1 = [];
202 var time = 1;
203
204 b.fi_x = ugol*j; //corner with an axis ОХ
205 b.omega=0;//angular velocity
206 var dx = diag*Math.cos(b.fi_x*Math.PI/180);//shift for drawing.
207 j=j*(-1);
208 b.x = (w / 2)-diag*(2*i+1)*(1.0+sm_x/100); b.y = h / (2.00+sm_y/100); // calculated coordinates of a sphere
209 b.Fx=0;b.Fy=0;
210 b.x_ = b.x; b.y_ = b.y;
211 b.fx = 0; b.fy = 0; // force operating on a sphere
212 b.vx = vx0; b.vy = vy0; // initial velocity
213 b1.fi_x = ugol*j; //corner with an axis OX
214 b1.omega=0;
215 b1.Fx=0;b1.Fy=0;
216 b1.x = (w / 2)+diag*(2*i+1)*(1.0+sm_x/100); b1.y = h / (2.00-sm_y/100) ; // calculated coordinates of a sphere
217 b1.x_ = b.x; b1.y_ = b.y;
218 b1.fx = 0; b1.fy = 0; // force operating on a sphere
219 b1.vx = vx0; b1.vy = vy0; // initial velocity
220 balls[n/2-(i+1)]=b;//[2*i]
221 balls[n/2+(i)] = b1;//[2*i+1]
222
223 }
224 }
225 this.set_c_d = function(input)
226 {
227 c_d = Number(input);
228 B_2 = c_d*diag*diag;
229 time = 1;
230 for (i = 0;i<n/2;i++)
231 {
232 var b = [];
233 var b1 = [];
234 var time = 1;
235
236 b.fi_x = 10*j; //corner with an axis OX
237 b.omega=0;//angular velocity
238 var dx = diag*Math.cos(b.fi_x*Math.PI/180);//shift for drawing.
239 j=j*(-1);
240 b.x = (w / 2)-diag*(2*i+1)*1.0; b.y = h / 2.00; // calculated coordinates of a sphere
241 b.Fx=0;b.Fy=0;
242 b.x_ = b.x; b.y_ = b.y;
243 b.fx = 0; b.fy = 0; // force operating on a sphere
244 b.vx = vx0; b.vy = vy0; // initial velocity
245 b1.fi_x = 10*j; //corner with an axis OX
246 b1.omega=0;
247 b1.Fx=0;b1.Fy=0;
248 b1.x = (w / 2)+diag*(2*i+1)*1.0; b1.y = h / 2 ; // calculated coordinates of a sphere
249 b1.x_ = b.x; b1.y_ = b.y;
250 b1.fx = 0; b1.fy = 0; // force operating on a sphere
251 b1.vx = vx0; b1.vy = vy0; // initial velocity
252 balls[n/2-(i+1)]=b;//[2*i]
253 balls[n/2+(i)] = b1;//[2*i+1]
254 }
255 context.clearRect(0, 0, w * scale, h * scale);
256 }
257 this.set_c_t = function(input)
258 {
259 c_t = Number(input);
260 B_4 = c_t;
261 time = 1;
262 for (i = 0;i<n/2;i++)
263 {
264 var b = [];
265 var b1 = [];
266 var time = 1;
267
268 b.fi_x = ugol*j; //corner with an axis OX
269 b.omega=0;//angular velocity
270 var dx = diag*Math.cos(b.fi_x*Math.PI/180);//shift for drawing.
271 j=j*(-1);
272 b.x = (w / 2)-diag*(2*i+1)*(1.0+sm_x/100); b.y = h / (2.00+sm_y/100); // calculated coordinates of a sphere
273
274 b.Fx=0;b.Fy=0;
275 b.x_ = b.x; b.y_ = b.y;
276 b.fx = 0; b.fy = 0; // force operating on a sphere
277 b.vx = vx0; b.vy = vy0; // initial velocity
278 b1.fi_x = ugol*j; //corner with an axis OX
279 b1.omega=0;
280 b1.Fx=0;b1.Fy=0;
281 b1.x = (w / 2)+diag*(2*i+1)*(1.0+sm_x/100); b1.y = h / (2.00-sm_y/100) ; // calculated coordinates of a sphere
282 b1.x_ = b.x; b1.y_ = b.y;
283 b1.fx = 0; b1.fy = 0; // force operating on a sphere
284 b1.vx = vx0; b1.vy = vy0; // initial velocity
285 balls[n/2-(i+1)]=b;//[2*i]
286 balls[n/2+(i)] = b1;//[2*i+1]
287 }
288 context.clearRect(0, 0, w * scale, h * scale);
289 }
290
291 slider_input.oninput = function() {
292 ugol = slider_input.value;
293 time = 1;
294 for (i = 0;i<n/2;i++)
295 {
296 var b = [];
297 var b1 = [];
298 var time = 1;
299 switch (f)
300 {
301 case 0:
302 b.fi_x = ugol*j;
303 b.x = (w / 2)-diag*(2*i+1)*(1.0+sm_x/100); b.y = h / (2.00+sm_y/100);
304 j=j*(-1);
305 b1.fi_x = ugol*j; //corner with an axis OX
306 b1.x = (w / 2)+diag*(2*i+1)*(1.0+sm_x/100); b1.y = h / (2.00-sm_y/100) ;
307 break;
308 case 1:
309 if (i ==((n/2)-1))//fixing of edge
310 {
311 b.x = (w / 2)-diag*(2*i+1)*1.0; b.y = h / 2.0;
312 b.fi_x = 0;
313 b1.fi_x = ugol*j; //corner with an axis OX
314 b1.x = (w / 2)+diag*(2*i+1)*(1.0+sm_x/100); b1.y = h / (2.00-sm_y/100) ;
315 }
316 else
317 {
318 b.fi_x = ugol*j;
319 b.x = (w / 2)-diag*(2*i+1)*(1.0+sm_x/100); b.y = h / (2.00+sm_y/100); // calculated coordinates of a sphere
320 j=j*(-1);
321 b1.fi_x = ugol*j; //corner with an axis OX
322 b1.x = (w / 2)+diag*(2*i+1)*(1.0+sm_x/100); b1.y = h / (2.00-sm_y/100) ;
323 }
324 break;
325 case 2:
326 if (i ==((n/2)-1))//fixing of edges
327 {
328 b.x = (w / 2)-diag*(2*i+1)*1.0; b.y = h / 2.0;
329 b.fi_x = 0;
330 b1.x = (w / 2)+diag*(2*i+1)*1.0; b1.y = h / 2.0;
331 b1.fi_x = 0;
332 }
333 else
334 {
335 b.fi_x = ugol*j;
336 b.x = (w / 2)-diag*(2*i+1)*(1.0+sm_x/100); b.y = h / (2.00+sm_y/100); // calculated coordinates of a sphere
337 j=j*(-1);
338 b1.fi_x = ugol*j; //corner with an axis OX
339 b1.x = (w / 2)+diag*(2*i+1)*(1.0+sm_x/100); b1.y = h / (2.00-sm_y/100) ;
340 }
341 break;
342 }
343 var dx = diag*Math.cos(b.fi_x*Math.PI/180);//shift for drawing.
344 b.omega=0;
345 b.Fx=0;b.Fy=0;
346 b.x_ = b.x; b.y_ = b.y;
347 b.fx = 0; b.fy = 0; // force operating on a sphere
348 b.vx = vx0; b.vy = vy0; // initial velocity
349 b1.omega=0;
350 b1.Fx=0;b1.Fy=0;
351 b1.x_ = b.x; b1.y_ = b.y;
352 b1.fx = 0; b1.fy = 0; // force operating on a sphere
353 b1.vx = vx0; b1.vy = vy0; // initial velocity
354 balls[n/2-(i+1)]=b;//[2*i]
355 balls[n/2+(i)] = b1;//[2*i+1]
356
357 }
358 context.clearRect(0, 0, w * scale, h * scale);
359 };
360
361 slider_input_ox.oninput = function() {
362 sm_x = slider_input_ox.value;
363 time = 1;
364 j=1;
365 for (i = 0;i<n/2;i++)
366 {
367 var b = [];
368 var b1 = [];
369 var time = 1;
370 switch (f)
371 {
372 case 0:
373 b.fi_x = ugol*j;
374 b.x = (w / 2)-diag*(2*i+1)*(1.0+sm_x/100); b.y = h / (2.00+sm_y/100);
375 j=j*(-1);
376 b1.fi_x = ugol*j; //corner with an axis OX
377 b1.x = (w / 2)+diag*(2*i+1)*(1.0+sm_x/100); b1.y = h / (2.00-sm_y/100) ;
378 break;
379 case 1:
380 if (i ==((n/2)-1))//fixing of edge
381 {
382 b.x = (w / 2)-diag*(2*i+1)*1.0; b.y = h / 2.0;
383 b.fi_x = 0;
384 b1.fi_x = ugol*j; //corner with an axis OX
385 b1.x = (w / 2)+diag*(2*i+1)*(1.0+sm_x/100); b1.y = h / (2.00-sm_y/100) ;
386 }
387 else
388 {
389 b.fi_x = ugol*j;
390 b.x = (w / 2)-diag*(2*i+1)*(1.0+sm_x/100); b.y = h / (2.00+sm_y/100); // calculated coordinates of a sphere
391 j=j*(-1);
392 b1.fi_x = ugol*j; //corner with an axis OX
393 b1.x = (w / 2)+diag*(2*i+1)*(1.0+sm_x/100); b1.y = h / (2.00-sm_y/100) ;
394 }
395 break;
396 case 2:
397 if (i ==((n/2)-1))//fixing of edges
398 {
399 b.x = (w / 2)-diag*(2*i+1)*1.0; b.y = h / 2.0;
400 b.fi_x = 0;
401 b1.x = (w / 2)+diag*(2*i+1)*1.0; b1.y = h / 2.0;
402 b1.fi_x = 0;
403 }
404 else
405 {
406 b.fi_x = ugol*j;
407 b.x = (w / 2)-diag*(2*i+1)*(1.0+sm_x/100); b.y = h / (2.00+sm_y/100); // calculated coordinates of a sphere
408 j=j*(-1);
409 b1.fi_x = ugol*j; //corner with an axis OX
410 b1.x = (w / 2)+diag*(2*i+1)*(1.0+sm_x/100); b1.y = h / (2.00-sm_y/100) ;
411 }
412 break;
413 }
414 b.omega=0;//angular velocity
415 var dx = diag*Math.cos(b.fi_x*Math.PI/180);//shift for drawing.
416 b.Fx=0;b.Fy=0;
417 b.x_ = b.x; b.y_ = b.y;
418 b.fx = 0; b.fy = 0; // force operating on a sphere
419 b.vx = vx0; b.vy = vy0; // initial velocity
420 b1.omega=0;
421 b1.Fx=0;b1.Fy=0;
422 b1.x_ = b.x; b1.y_ = b.y;
423 b1.fx = 0; b1.fy = 0; // force operating on a sphere
424 b1.vx = vx0; b1.vy = vy0; // initial velocity
425 balls[n/2-(i+1)]=b;//[2*i]
426 balls[n/2+(i)] = b1;//[2*i+1]
427 }
428 context.clearRect(0, 0, w * scale, h * scale);
429 };
430
431 slider_input_oy.oninput = function() {
432 sm_y = slider_input_oy.value;
433 time = 1;
434 j=1;
435 for (i = 0;i<n/2;i++)
436 {
437 var b = [];
438 var b1 = [];
439 var time = 1;
440 switch (f)
441 {
442 case 0:
443 b.fi_x = ugol*j;
444 b.x = (w / 2)-diag*(2*i+1)*(1.0+sm_x/100); b.y = h / (2.00+sm_y/100);
445 j=j*(-1);
446 b1.fi_x = ugol*j; //corner with an axis OX
447 b1.x = (w / 2)+diag*(2*i+1)*(1.0+sm_x/100); b1.y = h / (2.00-sm_y/100) ;
448 break;
449 case 1:
450 if (i ==((n/2)-1))//fixing of edge
451 {
452 b.x = (w / 2)-diag*(2*i+1)*1.0; b.y = h / 2.0;
453 b.fi_x = 0;
454 b1.fi_x = ugol*j; //corner with an axis OX
455 b1.x = (w / 2)+diag*(2*i+1)*(1.0+sm_x/100); b1.y = h / (2.00-sm_y/100) ;
456 }
457 else
458 {
459 b.fi_x = ugol*j;
460 b.x = (w / 2)-diag*(2*i+1)*(1.0+sm_x/100); b.y = h / (2.00+sm_y/100); // calculated coordinates of a sphere
461 j=j*(-1);
462 b1.fi_x = ugol*j; //corner with an axis OX
463 b1.x = (w / 2)+diag*(2*i+1)*(1.0+sm_x/100); b1.y = h / (2.00-sm_y/100) ;
464 }
465 break;
466 case 2:
467 if (i ==((n/2)-1))//fixing of edges
468 {
469 b.x = (w / 2)-diag*(2*i+1)*1.0; b.y = h / 2.0;
470 b.fi_x = 0;
471 b1.x = (w / 2)+diag*(2*i+1)*1.0; b1.y = h / 2.0;
472 b1.fi_x = 0;
473 }
474 else
475 {
476 b.fi_x = ugol*j;
477 b.x = (w / 2)-diag*(2*i+1)*(1.0+sm_x/100); b.y = h / (2.00+sm_y/100); // calculated coordinates of a sphere
478 j=j*(-1);
479 b1.fi_x = ugol*j; //corner with an axis OX
480 b1.x = (w / 2)+diag*(2*i+1)*(1.0+sm_x/100); b1.y = h / (2.00-sm_y/100) ;
481 }
482 break;
483 }
484 b.omega=0;//angular velocity
485 var dx = diag*Math.cos(b.fi_x*Math.PI/180);//shift for drawing.
486 b.Fx=0;b.Fy=0;
487 b.x_ = b.x; b.y_ = b.y;
488 b.fx = 0; b.fy = 0; // force operating on a sphere
489 b.vx = vx0; b.vy = vy0; // initial velocity
490 b1.omega=0;
491 b1.Fx=0;b1.Fy=0;
492 b1.x_ = b.x; b1.y_ = b.y;
493 b1.fx = 0; b1.fy = 0; // force operating on a sphere
494 b1.vx = vx0; b1.vy = vy0; // initial velocity
495 balls[n/2-(i+1)]=b;//[2*i]
496 balls[n/2+(i)] = b1;//[2*i+1]
497
498 }
499 context.clearRect(0, 0, w * scale, h * scale);
500 };
501 // The function doing spf of integration steps
502 function physics()
503 { // the fact that there is each step of time
504 for (var s = 1; s <= spf; s++) //integration step
505 {
506
507 for (i = 0;i<(n-1);i++)
508 {
509
510 d =[];
511 R = 1;
512 b = balls[i];//balls[2*i];
513 b1 = balls[i+1];//balls[2*i+1];
514 D = Math.sqrt((b.x-b1.x)*(b.x-b1.x)+(b.y-b1.y)*(b.y-b1.y));//Math.abs((b.x-b1.x));//Math.sqrt((b.x-b1.x)*(b.x-b1.x)+(b.y-b1.y)*(b.y-b1.y))-2*diag;
515 d.fi_x = 180*Math.asin((b1.y-b.y)/D)/3.14;
516 pr = 3.14/180;
517 fi = 180+b1.fi_x
518
519 //=============================================Силы=====================================
520 A = -Math.cos(inRad(fi))*Math.cos(inRad(d.fi_x))-Math.sin(inRad(fi))*Math.sin(inRad(d.fi_x))+Math.cos(inRad(b.fi_x))*Math.cos(inRad(d.fi_x))+Math.sin(inRad(b.fi_x))*Math.sin(inRad(d.fi_x));
521 b.Fx = B_1*(D-2*diag)*Math.cos(inRad(d.fi_x))+(B_2/2/D)*( Math.cos(inRad(fi))-Math.cos(inRad(b.fi_x))+A*Math.cos(inRad(d.fi_x)));
522 b1.Fx = -b.Fx;
523 b.Fy = B_1*(D-2*diag)*Math.sin(inRad(d.fi_x))+(B_2/2/D)*( Math.sin(inRad(fi))-Math.sin(inRad(b.fi_x))+A*Math.sin(inRad(d.fi_x)));
524 b1.Fy = -b.Fy;
525 M_tb = B_3*(Math.cos(inRad(fi))*Math.sin(inRad(b.fi_x))-Math.cos(inRad(b.fi_x))*Math.sin(inRad(fi)))-(B_4/2)*(Math.cos(inRad(fi-90))*Math.sin(inRad(b.fi_x+90))-Math.sin(inRad(fi-90))*Math.cos(inRad(b.fi_x+90)));
526 b.fx = R * (b.Fy*Math.cos(inRad(b.fi_x))-b.Fx*Math.sin(inRad(b.fi_x))) - (B_2/2) * (Math.cos(inRad(d.fi_x))*Math.sin(inRad(b.fi_x))-Math.sin(inRad(d.fi_x))*Math.cos(inRad(b.fi_x))) + M_tb;
527 b1.fx = R * (-Math.cos(inRad(fi))*b.Fy+Math.sin(inRad(fi))*b.Fx) + (B_2/2) * (Math.cos(inRad(d.fi_x))*Math.sin(inRad(fi))-Math.sin(inRad(d.fi_x))*Math.cos(inRad(fi)))- M_tb;
528
529 //======================================================================================
530 var J1 = 10000;
531 var m =1;
532 var beta_vr=0.00001//0.005;
533 var beta_x=0.5//1;
534 var beta_y=0.01//0.1;
535 //console.log(c_b);
536 if (f==0)//the free body
537 {
538 x_v1=balls[i].vx;
539 y_v1=balls[i].vy;
540 x_v2=balls[i+1].vx;
541 y_v2=balls[i+1].vy;
542 vr1 = balls[i].omega;
543 vr2 = balls[i+1].omega;
544 balls[i] = b;
545 balls[i+1] = b1;
546 balls[i].omega+=J1*(balls[i].fx-beta_vr*vr1)*dt;
547 balls[i].vx+=m*(balls[i].Fx-beta_x*x_v1)*dt;
548 balls[i].vy+=m*(balls[i].Fy-beta_y*y_v1)*dt;
549 balls[i+1].omega+=J1*(balls[i+1].fx-beta_vr*vr2)*dt;
550 balls[i+1].vx+=m*(balls[i+1].Fx-beta_x*x_v2)*dt;
551 balls[i+1].vy+=m*(balls[i+1].Fy-beta_y*y_v2)*dt;
552 balls[i].y+=balls[i].vy*dt;
553 balls[i].fi_x+=balls[i].omega*dt;
554 balls[i].x+=balls[i].vx*dt;
555 balls[i+1].x+=balls[i+1].vx*dt;
556 balls[i+1].fi_x+=balls[i+1].omega*dt;
557 balls[i+1].y+=balls[i+1].vy*dt;
558 asd=balls[0].fx+balls[1].fx;
559 }
560 else//the fixed edge
561 {
562 if (f==1)////the fixed edge
563 {
564 balls[i] = b;
565 balls[i+1] = b1;
566 x_v1=balls[i].vx;
567 y_v1=balls[i].vy;
568 x_v2=balls[i+1].vx;
569 y_v2=balls[i+1].vy;
570 vr1 = balls[i].omega;
571 vr2 = balls[i+1].omega;
572 balls[i].omega+=J1*(balls[i].fx-beta_vr*vr1)*dt;
573 balls[i].vx+=m*(balls[i].Fx-beta_x*x_v1)*dt;
574 balls[i].vy+=m*(balls[i].Fy-beta_y*y_v1)*dt;
575 balls[i+1].omega+=J1*(balls[i+1].fx-beta_vr*vr2)*dt;
576 balls[i+1].vx+=m*(balls[i+1].Fx-beta_x*x_v2)*dt;
577 balls[i+1].vy+=m*(balls[i+1].Fy-beta_y*y_v2)*dt;
578 if (i>0)
579 {
580 balls[i].fi_x+=balls[i].omega*dt;
581 balls[i+1].y+=balls[i+1].vy*dt;
582 balls[i].y+=balls[i].vy*dt;
583 balls[i].x+=balls[i].vx*dt;
584 balls[i+1].x+=balls[i+1].vx*dt;
585 balls[i+1].fi_x+=balls[i+1].omega*dt;
586 }
587 }
588 else //both edges are fixed
589 {
590
591 x_v1=balls[i].vx;
592 y_v1=balls[i].vy;
593 x_v2=balls[i+1].vx;
594 y_v2=balls[i+1].vy;
595 vr1 = balls[i].omega;
596 vr2 = balls[i+1].omega;
597 balls[i] = b;
598 balls[i+1] = b1;
599 balls[i].omega+=J1*(balls[i].fx-beta_vr*vr1)*dt;
600 balls[i].vx+=m*(balls[i].Fx-10*beta_x*x_v1)*dt;
601 balls[i].vy+=m*(balls[i].Fy-10*beta_y*y_v1)*dt;
602 balls[i+1].omega+=J1*(balls[i+1].fx-beta_vr*vr2)*dt;
603 balls[i+1].vx+=m*(balls[i+1].Fx-10*beta_x*x_v2)*dt;
604 balls[i+1].vy+=m*(balls[i+1].Fy-10*beta_y*y_v2)*dt;
605 if ((i>0)&&(i<(n-2)))
606 {
607 balls[i].fi_x+=balls[i].omega*dt;
608 balls[i+1].y+=balls[i+1].vy*dt;
609 balls[i].y+=balls[i].vy*dt;
610 balls[i].x+=balls[i].vx*dt;
611 balls[i+1].x+=balls[i+1].vx*dt;
612 balls[i+1].fi_x+=balls[i+1].omega*dt;
613 }
614
615 }
616 }
617
618 }
619
620 time = time + 1;
621 }
622 }
623 // definition of the function calculating force
624
625 // definition of function, risuyushchiy particle, walls and other
626 context.fillStyle = "#3070d0"; // colour
627 //===================================Interaction by a mouse========================
628 // function is started when pressing a key of a mouse
629 canvasBalls.onmousedown = function(e) {
630 var m = mouseCoords(e); // we receive cursor coordinates of a mouse
631 switch (f)
632 {
633 case(0):
634 var x = balls[n-1].x - m.x/scale; // distance from the center of a sphere to the cursor on an axis x
635 var y = balls[n-1].y - m.y/scale; // distance from the center of a sphere to the cursor on an axis y
636 var rLen2 = x * x + y * y; // distance square between the cursor and the center of a sphere
637 if (rLen2 <= diag*diag) { // if the cursor pressed a sphere
638 xShift = balls[n-1].x - m.x/scale; // shift of the cursor concerning the center of a sphere on x
639 yShift = balls[n-1].y - m.y/scale; // shift of the cursor concerning the center of a sphere for y
640 canvasBalls.onmousemove = mouseMove; // until the key is pressed - movement function works
641 }
642 break;
643 case(1):
644 var x = balls[n-1].x - m.x/scale; // distance from the center of a sphere to the cursor on an axis x
645 var y = balls[n-1].y - m.y/scale; // distance from the center of a sphere to the cursor on an axis y
646 var rLen2 = x * x + y * y; // distance square between the cursor and the center of a sphere
647 if (rLen2 <= diag*diag) { // if the cursor pressed a sphere
648 xShift = balls[n-1].x - m.x/scale; // shift of the cursor concerning the center of a sphere on x
649 yShift = balls[n-1].y - m.y/scale; // shift of the cursor concerning the center of a sphere for y
650 canvasBalls.onmousemove = mouseMove; // until the key is pressed - movement function works
651 }
652 break;
653 case (2):
654 case(0):
655 var x = balls[n/2].x - m.x/scale; // distance from the center of a sphere to the cursor on an axis x
656 var y = balls[n/2].y - m.y/scale; // distance from the center of a sphere to the cursor on an axis y
657 var rLen2 = x * x + y * y; // distance square between the cursor and the center of a sphere
658 if (rLen2 <= diag*diag) { // if the cursor pressed a sphere
659 xShift = balls[n/2].x - m.x/scale; // shift of the cursor concerning the center of a sphere on x
660 yShift = balls[n/2].y - m.y/scale; // shift of the cursor concerning the center of a sphere for y
661 canvasBalls.onmousemove = mouseMove; // until the key is pressed - movement function works
662 }
663 break;
664 }
665 };
666
667 // function is started at a key release of a mouse
668 document.onmouseup = function() {
669 canvasBalls.onmousemove = null; // when the key is released - there is no function of movement
670 };
671
672 // function is started when moving a mouse (many times, at every moment of movement)
673 // in our case works only with a viced key of a mouse
674 function mouseMove(e) {
675 switch (f)
676 {
677 case(0):
678 var m = mouseCoords(e); // we receive cursor coordinates of a mouse
679 balls[n-1].x = m.x/scale + xShift;
680 balls[n-1].y = m.y/scale+ yShift;
681 draw();
682 break;
683 case(1):
684 var m = mouseCoords(e);
685 x_nach =(w / 2)+diag*(n/2+2)*1.0;
686 y_nach = h / 2.0;
687 r_nach = Math.sqrt(x_nach*x_nach+y_nach*y_nach);
688 r_m = Math.sqrt(((m.x/scale-2*diag)-x_nach)*((m.x/scale-2*diag)-x_nach)+((m.y/scale)-y_nach)*((m.y/scale)-y_nach));
689 console.log(x_nach);
690 console.log(m.x/scale);
691 //console.log(r_nach);
692 if (Math.abs(r_m)<(3*diag)) // we receive cursor coordinates of a mouse
693 {pr_x = m.x/scale + xShift*0.01 -balls[n-1].x;
694 pr_y = m.y/scale+yShift-balls[n-1].y;
695 balls[n-1].x = m.x/scale + xShift*0.0001;
696 balls[n-1].y = m.y/scale+ yShift;
697 }
698 draw();
699 break;
700 case(2):
701 var m = mouseCoords(e); // we receive cursor coordinates of a mouse balls[n/2].x = m.x/scale + xShift;
702 balls[n/2].y = m.y/scale+ yShift;
703 draw();
704 break;
705 }
706 }
707
708 // function returns cursor coordinates of a mouse
709 function mouseCoords(e) {
710 var m = [];
711 var rect = canvasBalls.getBoundingClientRect();
712 m.x = e.clientX - rect.left;
713 m.y = e.clientY - rect.top;
714 //console.log(m.x/scale);
715 //console.log(balls[n-1].x);
716 return m;
717 }
718
719 function inRad(num)
720 {
721 return num * Math.PI / 180;
722 }
723
724 function draw()
725 {
726 context.clearRect(0, 0, w * scale, h * scale); // to clear the screen
727 for (var i =0;i<n;i++)
728 {
729 b = balls[i];
730 context.beginPath();
731 context.translate(b.x*scale,b.y * scale);//transfer in the center
732 context.rotate(inRad(b.fi_x-45));
733 context.fillRect(-rectW/2, -rectH/2, rectW, rectH);
734 context.rotate(-inRad(b.fi_x-45));
735 context.translate(-b.x * scale, -b.y * scale);//transfer back
736 context.closePath();
737 context.stroke();
738 }
739 }
740 }
File "v-model.html"
1 <!DOCTYPE html>
2 <html>
3 <head>
4 <title> Particle </title>
5 <script src="V_model.js"></script>
6 </head>
7 <body>
8 <!-- Addition of area for drawing of a particle -->
9 <canvas id="canvasBalls" width="800" height="400" style="border:1px solid #000000;"></canvas>
10
11 <div>
12 c_a =
13 <input id="Text_vx0" value = "100" style="width: 4.2ex;" required pattern="[-+]?([0-9]*\.[0-9]+|[0-9]+)" oninput="
14 if (!this.checkValidity()) return;
15 app.set_c_a(this.value);
16 <!-- document.getElementById('Slider_02').value = this.value; -->
17 ">
18 <!-- Addition of a slider -->
19 <!-- <input type="range" id="Slider_02" style="width: 100px;" oninput="app.set_02(this.value); document.getElementById('Text_02').value = this.value;"> -->
20 </I></font>
21 c_b =
22 <input id="Text_vx0" value = "0.1" style="width: 4.2ex;" required pattern="[-+]?([0-9]*\.[0-9]+|[0-9]+)" oninput="
23 if (!this.checkValidity()) return;
24 app.set_c_b(this.value);
25 <!-- document.getElementById('Slider_02').value = this.value; -->
26 ">
27 <!-- Addition of a slider -->
28 <!-- <input type="range" id="Slider_02" style="width: 100px;" oninput="app.set_02(this.value); document.getElementById('Text_02').value = this.value;"> -->
29 </I></font>
30 c_d =
31 <input id="Text_vx0" value = "100" style="width: 4.2ex;" required pattern="[-+]?([0-9]*\.[0-9]+|[0-9]+)" oninput="
32 if (!this.checkValidity()) return;
33 app.set_c_d(this.value);
34 <!-- document.getElementById('Slider_02').value = this.value; -->
35 ">
36 <!-- Addition of a slider -->
37 <!-- <input type="range" id="Slider_02" style="width: 100px;" oninput="app.set_02(this.value); document.getElementById('Text_02').value = this.value;"> -->
38 </I></font>
39 c_t =
40 <input id="Text_vx0" value = "1" style="width: 4.2ex;" required pattern="[-+]?([0-9]*\.[0-9]+|[0-9]+)" oninput="
41 if (!this.checkValidity()) return;
42 app.set_c_t(this.value);
43 <!-- document.getElementById('Slider_02').value = this.value; -->
44 ">
45 <!-- Addition of a slider -->
46 <!-- <input type="range" id="Slider_02" style="width: 100px;" oninput="app.set_02(this.value); document.getElementById('Text_02').value = this.value;"> -->
47 </I></font>
48 <input type="button" name="" onclick="
49 app.new_start();" value="restart"/></div>
50 <div><input type="radio" id="radio_pic_1" name="pic" checked /> Free body
51 <input type="radio" id="radio_pic_2" name="pic" /> Fixed edge
52 <input type="radio" id="radio_pic_3" name="pic" /> Fixed edges <br></div>
53 <div>Angle of torsion
54 0
55 <input type="range" id="slider_input" min=0 max=40 value=0 step=0.5 style="width: 200px;">40
56 <div>Shear OX
57 0
58 <input type="range" id="slider_input_ox" min=0 max=10 value=0 step=0.5 style="width: 200px;">10</div>
59 <div>Shear OY
60 0
61 <input type="range" id="slider_input_oy" min=0 max=10 value=0 step=0.5 style="width: 200px;">10</div>
62 <script type="text/javascript"> app = new MainParticle(document.getElementById('canvasBalls'));
63 </script>
64 </body>
65 </html>
