Мещерский Задача 7.2

Материал из Department of Theoretical and Applied Mechanics
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Мещерский Задача 7.2

Визуализация 3D-задачи по статике на JavaScript

Исполнитель: Киселёв Лев

Группа 23604/1 Кафедра Теоретической механики

Формулировка задачи[править]

По ребрам прямоугольного параллелепипеда действуют шесть сил. Привести эту систему к каноническому виду и определить координаты х и у точки пересечения центральной винтовой оси с плоскостью Оху.

Решение задачи[править]


<syntaxhighlight lang="javascript" line start="1" enclose="div">

<!DOCTYPE html> <head> 

       <script src = "http://tm.spbstu.ru/htmlets/Lebedev/Statika./three.js">
       </script>      
       <script src = "http://tm.spbstu.ru/htmlets/Lebedev/Statika./stats.min.js">
       </script>      
       <script src = "http://tm.spbstu.ru/htmlets/Lebedev/Statika./OrbitControls.js">
       </script>      
       <script src = "http://tm.spbstu.ru/htmlets/Lebedev/Statika./dat.gui.js">
       </script>


<style> body { margin:0; overflow:hidden; } </style>

<body>

<script>

var scene; var camera; var renderer; var axes; var cubeG ; var cubeM; var cube; var stats; var controls; var controls1; var arrowHelper = [];

var lx = 0; var ly = 0; var lz = 0;

var material; var geometry; var Box;

var Forces = []; for (var i = 1;i <= 6;i++) Forces[i] = [];

for (var i = 1;i <= 6;i++) { Forces[i][1] = new THREE.Vector3(0,0,0); //origin Forces[i][0] = new THREE.Vector3(0,0,0); //length }

function CountV_Force() { var tmp = new THREE.Vector3(0,0,0); for(var i = 1;i <= 6;i++) tmp.add(Forces[i][0]);

return tmp; }

function VxV(a,b) { var tmp = new THREE.Vector3(a.y*b.z - a.z*b.y,a.z*b.x - a.x*b.z,a.x*b.y - a.y*b.x); return tmp; }

function CountM() { var tmp = new THREE.Vector3(0,0,0); for (var i = 1;i <= 6;i++) { tmp.add(VxV(Forces[i][1],Forces[i][0])); } return tmp; }

function CountCross(R,p,M) { tmp = {x:(R.x*p - M.x)/(R.y),y:(-R.z*p + M.z)/(R.y)}; return tmp; } function Relog() { var tmpV = CountV_Force(); var tmpM = CountM();

var M = tmpM.dot(tmpV)/tmpV.length();

var tmp = CountCross(tmpV,M/tmpV.length(),tmpM);

var ex = new THREE.Vector3(0,0,1); var ey = new THREE.Vector3(1,0,0); var ez = new THREE.Vector3(0,1,0);

var res1 = tmpV.length().toFixed(3).toString(); var res2 = tmpV.normalize().dot(ex).toFixed(3).toString(); var res3 = tmpV.normalize().dot(ey).toFixed(3).toString(); var res4 = tmpV.normalize().dot(ez).toFixed(3).toString(); var res5 = M.toFixed(3).toString(); res6 = tmp.x.toFixed(3).toString(); res7 = tmp.y.toFixed(3).toString();

controls1.V = res1; controls1.cos1 = res2; controls1.cos2 = res3; controls1.cos3 = res4; controls1.M = res5; controls1.x = res6; controls1.y = res7;

console.log('V: ',res1, ' H; cos(a): ' , res2 , ' ; cos(b): ' , res3 , ' ; cos(phi): ' , res4 , ' ; M: ', res5 , ' H*м ; x : ' , res6 , ' м; y: ' , res7 , ' м;');

}


function SetDirOriginForces() { Forces[1][1].set(0,controls1.Lz,0); Forces[1][0].setX(controls1.Force1);

Forces[2][1].set(controls1.Ly,controls1.Lz,0); Forces[2][0].setZ(controls1.Force2);

Forces[3][1].set(controls1.Ly,controls1.Lz,controls1.Lx); Forces[3][0].setY(controls1.Force3);

Forces[4][1].set(controls1.Ly,0,controls1.Lx); Forces[4][0].setX(controls1.Force4);

Forces[5][1].set(0,0,controls1.Lx); Forces[5][0].setZ(controls1.Force5);

Forces[6][1].set(0,0,0); Forces[6][0].setY(controls1.Force6); }

function init() { scene = new THREE.Scene(); camera = new THREE.PerspectiveCamera(45,window.innerWidth/window.innerHeight,0.1,1000);

renderer = new THREE.WebGLRenderer(); renderer.setClearColor(0xEEEEEE,1); renderer.setSize(window.innerWidth,window.innerHeight);

axes = new THREE.AxisHelper(20); scene.add(axes);

camera.position.x = 20; camera.position.y = 20; camera.position.z = 30; camera.lookAt(scene.position); document.getElementById("WebGL").appendChild(renderer.domElement);

var slight1 = new THREE.SpotLight(0xffffff); slight1.position.set(-40,-40,40); scene.add(slight1);

var slight2 = new THREE.SpotLight(0xffffff); slight2.position.set(40,40,-40); scene.add(slight2);

controls1 = new function() { this.Force1 = 4; this.Force2 = 6; this.Force3 = -3; this.Force4 = -2; this.Force5 = -6; this.Force6 = 8;

this.Lx = 4; this.Ly = 10; this.Lz = 5;

this.V = '0';

this.cos1 = '0'; this.cos2 = '0'; this.cos3 = '0';

this.M = '0'; this.x = '0'; this.y = '0'; }

stats=initStats(); controls=new THREE.OrbitControls(camera,renderer.domElement); renderScene();

var gui = new dat.GUI();

var contr = gui.addFolder('Controls')

contr.add(controls1, 'Force1' , -10, 10).onChange(Relog); contr.add(controls1, 'Force2' , -10, 10).onChange(Relog); contr.add(controls1, 'Force3' , -10, 10).onChange(Relog); contr.add(controls1, 'Force4' , -10, 10).onChange(Relog); contr.add(controls1, 'Force5' , -10, 10).onChange(Relog); contr.add(controls1, 'Force6' , -10, 10).onChange(Relog);

contr.add(controls1, 'Lx' , 0, 50).onChange(Relog); contr.add(controls1, 'Ly' , 0, 50).onChange(Relog); contr.add(controls1, 'Lz' , 0, 50).onChange(Relog);


var res = gui.addFolder('Result');

res.add(controls1, 'V').listen(); res.add(controls1, 'cos1').listen(); res.add(controls1, 'cos2').listen(); res.add(controls1, 'cos3').listen(); res.add(controls1, 'M').listen(); res.add(controls1, 'x').listen(); res.add(controls1, 'y').listen();

Relog(); window.addEventListener('resize',onResize,false); };

function ClearScene() { scene.remove(Box); for (var i = 1;i <=6;i++) scene.remove(arrowHelper[i]); }

function renderScene() { stats.update(); requestAnimationFrame(renderScene);

lx = controls1.Ly; ly = controls1.Lz; lz = controls1.Lx;

ClearScene();

material = new THREE.LineBasicMaterial({ color: 0x0000ff });

geometry = new THREE.Geometry(); geometry.vertices.push( new THREE.Vector3( 0, 0, 0 ), new THREE.Vector3( lx, 0, 0 ), new THREE.Vector3( lx, ly, 0 ), new THREE.Vector3( 0 , ly, 0 ), new THREE.Vector3( 0, 0, 0 ),

new THREE.Vector3( 0, 0, lz ),

new THREE.Vector3( lx, 0, lz ), new THREE.Vector3( lx, 0, 0 ), new THREE.Vector3( lx, 0, lz ),

new THREE.Vector3( lx, ly, lz ), new THREE.Vector3( lx, ly, 0 ), new THREE.Vector3( lx, ly, lz ),

new THREE.Vector3( 0 , ly, lz ), new THREE.Vector3( 0 , ly, 0 ), new THREE.Vector3( 0 , ly, lz ),

new THREE.Vector3( 0, 0, lz ) );

Box = new THREE.Line( geometry, material ); scene.add( Box );

SetDirOriginForces();

for (var i = 1;i <=6;i++) { var dir = Forces[i][0].clone(); arrowHelper[i] = new THREE.ArrowHelper( Forces[i][0].clone().normalize(), Forces[i][1], Forces[i][0].clone().length()/2, 0xFF0000 , 0.40 , 0.40); scene.add(arrowHelper[i]); }

renderer.render(scene,camera); };

function initStats() { var stats=new Stats(); stats.setMode(0); stats.domElement.style.position="0px"; stats.domElement.style.left="0px"; stats.domElement.style.top="0px"; document.getElementById("Stats-output").appendChild(stats.domElement); return stats; };

function onResize() { camera.aspect=window.innerWidth/window.innerHeight; camera.updateProjectionMatrix(); renderer.setSize(window.innerWidth,window.innerHeight); }

window.onload = init; </script> </body>

</head>
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