Задача о двух телах

Материал из Department of Theoretical and Applied Mechanics
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Описание

Решение и визуализация задачи двух тел.

Шелых Екатерина

Файл:[[1]]

Код программы

Код программы

Текст программы на языке JavaScript:

<syntaxhighlight lang="javascript" line start="1" enclose="div"> var gravitationalConstant = 6.67*Math.pow(10,-11);//гравитационная постоянная var point_x1 = 1200/6*3; var point_y1 = 300; var point_x2 = 1200/6*4; var point_y2 = 300; var sP = 1; var k = 0; var flag = 0; function firstPaint(){ 

 var canvas = document.getElementById('pole');
 if (canvas.getContext){
     var ctx = canvas.getContext('2d');
 }
 var img1 = new Image();
     img1.src = "planet1.jpg";
 img1.onload = function(){

     var img = new Image();
         img.src = "space.jpg";
      img.onload = function(){
        var pattern = ctx.createPattern(img,"repeat");
           ctx.fillStyle = pattern;
           ctx.beginPath();
           ctx.clearRect(0,0,1500,800);
           ctx.moveTo(1,1);
           ctx.fillRect(0, 0, 1500, 800);
           ctx.closePath();
           ctx.beginPath();
           ctx.fillStyle = "#F6F231";
           ctx.arc(point_x1,point_y1,10,0,Math.PI*2);
           ctx.fill();
       var img2 = new Image();
           img2.src = "planet2.jpg";
       img2.onload = function(){
         var pattern2 = ctx.createPattern(img2,"repeat");
           ctx.beginPath();
           ctx.fillStyle = pattern2;

       ctx.moveTo(point_x2,point_y2);
       ctx.arc(point_x2,point_y2,10,0,Math.PI*2);
       ctx.fill();
     }
   }

}

} function AddPlanet(x,y,mass,speed){ 

 this.x = x;
 this.y = y;
 this.mass = mass;

 this.M = this.mass*gravitationalConstant;
 this.speed = speed;

} function makePlanets(){ 

  point_x1 = 1200/6*3;
  point_y1 = 300;
  point_x2 = 1200/6*4;
  point_y2 = 300;
 var mass =document.getElementById('firstMass').value*Math.pow(10,20);
 var speed = 1;
 var firstPlanet = new AddPlanet(point_x1,point_y1,mass,speed);
 mass = document.getElementById('secondMass').value*Math.pow(10,20);
 speed = 1;
 var secondPlanet = new AddPlanet(point_x1,point_y1,mass,speed);



 firstPlanet.r = Math.pow(10,7)*(point_x2 - point_x1 - (point_x2-point_x1)*firstPlanet.mass/(firstPlanet.mass + secondPlanet.mass));//радиус вектор 1 тела относительно центра масс системы
 secondPlanet.r =  Math.pow(10,7)*((point_x2-point_x1)*firstPlanet.mass/(firstPlanet.mass + secondPlanet.mass));//радиус вектор 1 тела относительно центра масс системы
 firstPlanet.massCenterX = point_x2 - (point_x2-point_x1)*firstPlanet.mass/(firstPlanet.mass + secondPlanet.mass);//рассчет x координыты центра масс
 firstPlanet.c = firstPlanet.speed*firstPlanet.r;//константы закона площадей
 secondPlanet.c = secondPlanet.speed*secondPlanet.r;//константы закона площадей



 firstPlanet.f = -firstPlanet.M + firstPlanet.speed*firstPlanet.c;//векторы Лапласса
 secondPlanet.f = -secondPlanet.M + secondPlanet.speed*secondPlanet.c;//векторы Лапласса

 firstPlanet.p = Math.pow(firstPlanet.c, 2)/firstPlanet.M/Math.pow(10,6); //фокальный параметр
 secondPlanet.p = Math.pow(secondPlanet.c, 2)/secondPlanet.M/Math.pow(10,6); //фокальный параметр

 firstPlanet.e = firstPlanet.f/firstPlanet.M;//эксцентриситет
 secondPlanet.e = secondPlanet.f/secondPlanet.M;//эксцентриситет
 console.log('e1=',firstPlanet.e,'e2=',secondPlanet.e);

 drawPlanets(firstPlanet,secondPlanet);

}

function drawPlanets(firstPlanet,secondPlanet){ 

 var canvas = document.getElementById('pole');
 if (canvas.getContext){
   var ctx = canvas.getContext('2d');
 }

 var img = new Image();
     img.src = "space.jpg";
 var img2 = new Image();
     img2.src = "planet2.jpg";

 var pattern2 = ctx.createPattern(img2,"repeat");

     img.onload = function() {
       var pattern = ctx.createPattern(img,"repeat");
       ctx.fillStyle = pattern;

       var angle = Math.PI;
       var angle2 = 0;

       firstPlanet.a = firstPlanet.p/(1 - firstPlanet.e)*6;
       firstPlanet.b = firstPlanet.p/Math.pow((1 - firstPlanet.e),0.5)*3;
       firstPlanet.c = Math.abs(firstPlanet.e*firstPlanet.a);//фокольное расстояние
         secondPlanet.a = secondPlanet.p/(1 - secondPlanet.e)*6;
         secondPlanet.b = secondPlanet.p/Math.pow((1 - secondPlanet.e),0.5)*3;
         secondPlanet.c = Math.abs(secondPlanet.e*secondPlanet.a);//фокольное расстояние
       firstPlanet.leftScope = firstPlanet.a*Math.cos(180);
       secondPlanet.scope = secondPlanet.a*Math.cos(0);
       point_x1 = firstPlanet.massCenterX + firstPlanet.c;
       point_x2 = firstPlanet.massCenterX - secondPlanet.c;

var x = 10, y = 390; 

       var timerId = setInterval( function(){
         if (k==2){
           var a =1;
         }
         else{
           angle = angle + Math.PI/360;
           if (angle >= 2*Math.PI){
                 angle = 0;
             }
             angle2 = angle2 + Math.PI/360;
             if (angle2 >= 2*Math.PI){
                 angle2 = 0;
               }
             firstPlanet.x = point_x1 + firstPlanet.a*Math.cos(angle);
             firstPlanet.y = point_y1 + firstPlanet.b*Math.sin(angle);

             secondPlanet.x = point_x2 + secondPlanet.a*Math.cos(angle2);
             secondPlanet.y = point_y2 + secondPlanet.b*Math.sin(angle2);
             ctx.fillStyle = pattern;
               ctx.beginPath();
               ctx.clearRect(0,0,1500,800);
               ctx.moveTo(1,1);
               ctx.fillRect(0, 0, 1500, 800);
               ctx.closePath();

             ctx.beginPath();
             ctx.moveTo(firstPlanet.x,firstPlanet.y);
             ctx.fillStyle = "#F6F231";
             ctx.arc(firstPlanet.x,firstPlanet.y,10,0,2*Math.PI);
             ctx.fill();

             ctx.beginPath();
             ctx.moveTo(firstPlanet.x,firstPlanet.y);
             ctx.fillStyle = pattern2;
             ctx.arc(secondPlanet.x ,secondPlanet.y ,10,0,2*Math.PI);
             ctx.fill();

             ctx.beginPath();
             ctx.moveTo(firstPlanet.massCenterX,point_y1);
             ctx.fillStyle = "#1D067F";
             ctx.arc(firstPlanet.massCenterX,point_y1 ,4,0,2*Math.PI);
             ctx.fill();

             y = graph1(firstPlanet,secondPlanet,x,y);
             x = x + 1;
             if (k==1){
               clearTimeout(timerId);
               k = 0;
             }
           }
         },sP);

       };

}


function breakk(){ 

 k = 1;

}


function pausee(){ 

 if (k==0){
   k = 2;
 }
 else{
   k = 0;
 }

}

function graph1(firstPlanet,secondPlanet,x,y){ 

 var canvas = document.getElementById('pole2');
 if (canvas.getContext){
     var canvas = canvas.getContext('2d');
 }


if ( flag == 0){ 

 canvas.beginPath();
 canvas.strokeStyle = "#000000";
 canvas.moveTo(10,395);
 canvas.lineTo(10,10);
 canvas.lineTo(5,15);
 canvas.moveTo(10,10);
 canvas.lineTo(15,15);
 canvas.moveTo(5,390);
 canvas.lineTo(690,390);
 canvas.lineTo(685,395);
 canvas.moveTo(690,390);
 canvas.lineTo(685,385);
 canvas.moveTo(550,20);
 canvas.lineTo(550,100);
 canvas.lineTo(690,100);
 canvas.lineTo(690,20);
 canvas.lineTo(550,20);
 canvas.strokeStyle = "#000000";
 canvas.font = "20px serif";
 canvas.fillText('R(t)',20,20);
 canvas.stroke();
 flag = 1;

} 

return lengAndDraw(firstPlanet,secondPlanet,canvas,x,y)

}


function lengAndDraw(firstPlanet,secondPlanet,canvas,x,y){ 

 var l = Math.sqrt( Math.pow(firstPlanet.x-secondPlanet.x,2) + Math.pow(firstPlanet.y - secondPlanet.y,2))/3.5;

// console.log(l); 

 canvas.beginPath();
 canvas.clearRect(550,20,140,80);
 canvas.strokeStyle = "#000000";
 canvas.moveTo(x,y);
 canvas.lineTo(x + 1, 390 - l);
 canvas.font = "20px serif";
 canvas.fillText('r = ' + Math.floor(l*3.5) + '*10^7', 570, 60);
 canvas.stroke();
  return (390 - l);

}

Источник — «http://tm.spbstu.ru/?title=Задача_о_двух_телах&oldid=53906»