Редактирование: Цепочка частиц с вращательными степенями свободы

[[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]]):'''