Цепочка из частиц с вращательными степенями свободы — различия между версиями

Материал из Department of Theoretical and Applied Mechanics
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[[Виртуальная лаборатория]] > '''[[Цепочка частиц с вращательными степенями свободы]]''' <HR>
 
  
== Краткое описание ==
 
 
Рассматривается совокупность твердых тел, образующих цепочки. Центры масс фиксированы. Взаимодействия осуществляются посредством балок Бернулли-Эйлера, соединяющих тела.
 
 
== Реализации цепочки ==
 
 
 
<div class="mw-collapsible mw-collapsed" style="width:100%" >
 
 
<div class="mw-collapsible-content">
 
<syntaxhighlight lang="javascript" line start="1" enclose="div">
 
 
window.addEventListener("load", MainSystem, true);
 
 
function MainSystem(){
 
var context_s = canvasSystem.getContext('2d');               
 
var context_g = canvasGraph.getContext('2d');               
 
var context_g_1 = canvasGraph_1.getContext('2d');
 
var context_g_2 = canvasGraph_2.getContext('2d');
 
 
const Pi = 3.1415926;                 
 
const m0 = 1;                       
 
const T0 = 1;                       
 
const l0 = 1;
 
const E0 = 1;
 
 
//Width of canvas - width of browser
 
const distance_between_canvases = 5;    //5px
 
canvasSystem.width = document.body.clientWidth; 
 
canvasGraph.width = document.body.clientWidth / 2 - distance_between_canvases;
 
canvasGraph_1.width = document.body.clientWidth / 2 - distance_between_canvases;
 
canvasGraph_2.width = document.body.clientWidth;
 
 
/* -- Used constans -- */
 
var Db = 0.1 * l0; // Diameter of beam
 
const l = 30 * l0; //Length of beam
 
const a = 60 * l0; //Length of object
 
var Db2 = Db * Db;
 
var J = Pi * Db2 * Db2 / 64;      //Polar moment of inertia
 
const E = 10000000 * E0; //Youngs modulus
 
var C = E * J / l;
 
var N = parseFloat(number_of_objects.value) + 1; //number_of_objects.value is number of objects
 
const m = 0.01 * m0;            //Mass of object
 
const Q = m * a * a / 12;  //Moment of inertia
 
const w_c = Math.sqrt(2 * C / Q);  //Self frequency
 
 
const fps = 50;                        // frames per second
 
  var spf = calcul_speed.value;          // steps per frame 
 
  const frequency = 1000 / fps; //frequency of call function - 1000 milliseconds/ fps
 
const dt  =  0.05 * T0 / fps;         //Step of integration 
 
 
var scale = canvasSystem.width / N;  //Scale of graph of system
 
var scale1 = canvasGraph_2.width / (N + 2); //Scale of graph of angels
 
 
//For wave
 
const n = 1;  //Number of full-wave
 
var k_ = 2 * Pi / (l * (N - 2) * n);  //Spatial frequencyw
 
var w_ = Math.sqrt((-2 * C / Q * l * l) * k_ * k_ + (12 * C / Q));
 
 
/* -- Used variables -- */
 
var K0 = 0; var P0 = 0; var E_p0 = 0; var L0 = 0; //Energies at  i-step
 
var K1 = 0; var P1 = 0; var E_p1 = 0; var L1 = 0; // Energies at (i+1)-step
 
var E_m = 0;    //Maximum of Energy at the first moment
 
var t = 0; //Time
 
 
var U = [];  //Exact solution for wave
 
var shaft = [];  //Objects
 
 
var pause = false;
 
const stretch_graphics = 3;
 
var help = stretch_graphics * canvasGraph.width; //Scale of graph of energies
 
var firstCalculation = true;
 
/* -- */
 
 
//Restart the programm with new parameters
 
restart.onclick = function(){
 
N = parseFloat(number_of_objects.value) + 1;
 
scale = canvasSystem.width / N;
 
scale1 = canvasGraph_2.width / (N + 2);
 
spf = calcul_speed.value;
 
J = Pi * Db2 * Db2 / 64;     
 
C = E * J / l;
 
 
context_s.clearRect(0, 0, canvasSystem.width, canvasSystem.height);
 
context_g.clearRect(0, 0, canvasGraph.width, canvasGraph.height);
 
context_g_1.clearRect(0, 0, canvasGraph_1.width, canvasGraph_1.height);
 
context_g_2.clearRect(0, 0, canvasGraph_2.width, canvasGraph_2.height);
 
 
shaft = [];
 
addSystem(shaft);
 
 
firstCalculation = true;
 
t = 0;
 
P1 = 0;
 
K1 = 0;
 
E_m = 0;
 
}
 
 
//Pause
 
pause_button.onclick = function(){
 
pause = !pause; 
 
if(pause == false)
 
pause_button.value = "Pause";
 
else
 
pause_button.value = "Run";
 
}
 
 
//Calculate all parameters of system
 
  function control(){
 
    if(!pause){
 
/* -- Find the maximum of energy -- */
 
if(firstCalculation){
 
for (var i = 1; i < N; i++){
 
E_m += Q * shaft[i].w * shaft[i].w / 2;
 
}
 
 
for (var i = 1; i < N; i++){
 
E_m +=  C / 2 * (12 * shaft[i].fi * shaft[i].fi - ((shaft[i-1].fi - shaft[i].fi) * (shaft[i-1].fi - shaft[i].fi) +
 
(shaft[i].fi - shaft[i+1].fi) * (shaft[i].fi - shaft[i+1].fi)));
 
}
 
 
L0 = E_m;
 
E_p0 = E_m / 2;
 
firstCalculation = false;
 
}
 
/* -- */
 
 
physics();
 
draw();
 
 
if(t*help > canvasGraph.width){
 
t = 0;
 
context_g.clearRect(0, 0, canvasGraph.width, canvasGraph.height);
 
context_g_1.clearRect(0, 0, canvasGraph_1.width, canvasGraph_1.height);
 
}
 
 
draw_Graph_energy(t*help, (t + dt)*help);
 
draw_Graph_angels();
 
 
//exact_solution_for_wave(t*help);
 
 
P0 = P1;
 
K0 = K1;
 
L0 = L1;
 
E_p0 = E_p1;
 
E_p1 = 0;
 
L1 = 0;
 
P1 = 0;
 
K1 = 0;
 
t += dt;
 
}
 
  }
 
 
//Physics - calculate the positions of objects
 
function physics(){
 
    for (var s = 1; s <= spf; s++){
 
    //Periodic initial conditions
 
shaft[0].fi = shaft[N-1].fi;
 
shaft[N].fi = shaft[1].fi;
 
 
for (var i = 1; i < N; i++){
 
shaft[i].M = - 2 * C * (shaft[i-1].fi + 2 * shaft[i].fi) - 2 * C * (2 * shaft[i].fi + shaft[i+1].fi);
 
}
 
 
for (var i = 1; i < N; i++){
 
shaft[i].w += shaft[i].M / Q * dt;
 
shaft[i].fi += shaft[i].w * dt;
 
}
 
 
for (var i = 1; i < N; i++){
 
shaft[i].M = 0;
 
}
 
  }
 
  }
 
 
//Draw the graph of system
 
function draw(){
 
    context_s.clearRect(0, 0, canvasSystem.width, canvasSystem.height);
 
 
    for (var i = 1; i < N; i++){
 
context_s.beginPath();
 
context_s.moveTo(shaft[i].x - (a/2) * Math.sin(shaft[i].fi), shaft[i].y - (a/2) * Math.cos(shaft[i].fi));
 
context_s.lineTo(shaft[i].x + (a/2) * Math.sin(shaft[i].fi), shaft[i].y + (a/2) * Math.cos(shaft[i].fi));
 
context_s.closePath();
 
context_s.stroke();
 
    }
 
  }
 
 
//Draw the graph of angels
 
function draw_Graph_angels(){
 
context_g_2.clearRect(0, 0, canvasGraph_2.width, canvasGraph_2.height); 
 
 
for(var i = 0; i < N; i++){
 
context_g_2.beginPath();
 
context_g_2.moveTo(scale1 * (i+1), -shaft[i].fi / (Pi/2) * canvasGraph_2.height / 2 + canvasGraph_2.height / 2);
 
context_g_2.lineTo(scale1 * (i+2), -shaft[i+1].fi / (Pi/2) * canvasGraph_2.height / 2 + canvasGraph_2.height / 2);
 
context_g_2.closePath();
 
context_g_2.stroke();
 
}
 
}
 
 
//Draw the graphics of energies
 
function draw_Graph_energy(x0, x1){
 
//Potential
 
context_g_1.beginPath();
 
context_g_1.strokeStyle = "#FF0000";
 
context_g_1.moveTo(x0, -P0 / E_m * canvasGraph_1.height + canvasGraph_1.height);
 
 
for (var i = 1; i < N; i++){
 
P1 +=  C / 2 * (12 * shaft[i].fi * shaft[i].fi - ((shaft[i-1].fi - shaft[i].fi) * (shaft[i-1].fi - shaft[i].fi) +
 
(shaft[i].fi - shaft[i+1].fi) * (shaft[i].fi - shaft[i+1].fi)));
 
}
 
 
context_g_1.lineTo(x1, -P1 / E_m * canvasGraph_1.height + canvasGraph_1.height);
 
context_g_1.closePath();
 
context_g_1.stroke();
 
 
//Kinetical
 
context_g_1.beginPath();
 
context_g_1.strokeStyle = "#000000";
 
context_g_1.moveTo(x0, -K0 / E_m * canvasGraph_1.height + canvasGraph_1.height);
 
 
for (var i = 1; i < N; i++){
 
K1 += Q * shaft[i].w * shaft[i].w / 2;
 
}
 
 
context_g_1.lineTo(x1, -K1 / E_m * canvasGraph_1.height + canvasGraph_1.height);
 
context_g_1.closePath();
 
context_g_1.stroke();
 
 
//Full energy
 
context_g_1.beginPath();
 
context_g_1.strokeStyle = "blue";
 
context_g_1.moveTo(x0, -E_p0 / E_m * canvasGraph.height + canvasGraph.height);
 
 
E_p1 = (K1 + P1) / 2;
 
 
context_g_1.lineTo(x1, -E_p1 / E_m * canvasGraph.height + canvasGraph.height);
 
context_g_1.closePath();
 
context_g_1.stroke();
 
 
//Lagrangian
 
context_g.beginPath();
 
context_g.strokeStyle = "orange";
 
context_g.moveTo(x0, -L0 / E_m * canvasGraph.height / 2 + canvasGraph.height / 2);
 
 
L1 = K1 - P1;
 
 
context_g.lineTo(x1, -L1 / E_m * canvasGraph.height / 2 + canvasGraph.height / 2);
 
context_g.closePath();
 
context_g.stroke();
 
}
 
 
    //Add the system of objects
 
  function addSystem(shaft){
 
  for (var i = 0; i < N + 1; i++){
 
var shaft_new = [];
 
 
shaft_new.x = scale * i;         
 
shaft_new.y = canvasSystem.height / 2;
 
shaft_new.fi = 0;
 
shaft_new.w = 0;
 
shaft_new.M = 0;
 
shaft[shaft.length] = shaft_new;  
 
}
 
 
/*  --Initial conditions-- */
 
//Random velocities
 
if(all_.checked){
 
var average_w = 0; //Average velocity
 
 
for (var i = 0; i < N; i++){
 
shaft[i].w = Math.random() * w_c;
 
average_w += shaft[i].w;
 
}
 
 
average_w /= N;
 
 
for (var i = 0; i < N; i++){
 
shaft[i].w -= average_w;
 
}
 
}
 
 
// N/10 - Central part of objects by sin
 
if(part.checked){
 
for (var i = Math.floor(-Math.floor(N / 10) / 2); i < Math.floor(Math.floor(N / 10) / 2); i++){
 
shaft[Math.floor(N / 2) + i + 1].fi =
 
Math.sin(2 * Pi * (Math.floor(Math.floor(N / 10) / 2) - i) * (Math.floor(Math.floor(N / 10) / 2) + i) / N/2);
 
}
 
}
 
 
//Central object
 
if(one.checked){
 
shaft[Math.floor(N / 2)].w = w_c;
 
}
 
 
//Wave
 
if(wave.checked){
 
for (var i = 1; i < N; i++){
 
shaft[i].fi = Math.sin(k_ * (l * i));
 
shaft[i].w = -w_ * Math.cos(k_ * (l * i));
 
}
 
}
 
  }
 
 
//Exact solution for wave
 
function exact_solution_for_wave(t) {
 
for (var i = 1; i < N; i++){
 
U[i] = Math.sin(k_ * (l * i) - w_ * t / 200);
 
}
 
//context_g_2.clearRect(0, 0, canvasGraph_2.width, canvasGraph_2.height);
 
for(var i = 0; i < N; i++){
 
context_g_2.beginPath();
 
context_g_2.moveTo(scale1 * (i+1), -U[i] / (Pi/2) * canvasGraph_2.height / 2 + canvasGraph_2.height / 2);
 
context_g_2.lineTo(scale1 * (i+2), -U[i+1] / (Pi/2) * canvasGraph_2.height / 2 + canvasGraph_2.height / 2);
 
context_g_2.closePath();
 
context_g_2.stroke();
 
}
 
}
 
 
addSystem(shaft);      //Adding our system of objects
 
 
  setInterval(control, frequency); 
 
}
 
</syntaxhighlight>
 
 
<syntaxhighlight lang="html5" line start="1" enclose="div">
 
<!DOCTYPE html>
 
<html>
 
<body>
 
<canvas id="canvasSystem" width="1200" height="300" style="border:1px solid #000000;"></canvas><br><br>
 
 
Number of objects: <input type="number" id="number_of_objects" value="500" step=1 style="width: 5em">,
 
Calculation speed: <input type="range" id="calcul_speed" value="100" step=0.01 min=10 max=300><br>
 
 
Initial conditions:<br>
 
<input type="radio" checked="checked" name="initial_conditions" id="all_"/>Random velocities<br>
 
<input type="radio"  name="initial_conditions" id="part"/>Central part of objects by sin<br>
 
<input type="radio" name="initial_conditions" id="one"/>One object<br>
 
<input type="radio" name="initial_conditions" id="wave"/>Wave<br>
 
<input type="button" id="restart" value="Restart">
 
<input type="button" id="pause_button" value="Pause"><br><br>
 
 
Graphics:<br>
 
<canvas id="canvasGraph" width="600" height="300" style="border:1px solid #000000;"></canvas>
 
<canvas id="canvasGraph_1" width="600" height="300" style="border:1px solid #000000;"></canvas><br>
 
L<hr align="left" width="50" size="3" color="orange" />
 
E / 2<hr align="left" width="50" size="3" color="blue" />
 
K<hr align="left" width="50" size="3" color="#000000" />
 
P<hr align="left" width="50" size="3" color="#FF0000" /><br>
 
 
Angles:<br>
 
<canvas id="canvasGraph_2" width="1200" height="300" style="border:1px solid #000000;"></canvas><br>
 
 
<script src="simulation.js"></script>
 
</body>
 
</html>
 
</syntaxhighlight>
 
</div>
 
</div>
 
[https://bitbucket.org/GA__GA/spin-degree-of-freedom/get/c518f9b3fb9b.zip Скачать архив]
 
'''Текст программы на языке JavaScript (разработчик [[Александров Александр]]):'''
 

Текущая версия на 20:10, 22 мая 2016