Мещерский Задача 7.10 — различия между версиями

Материал из Department of Theoretical and Applied Mechanics
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(не показано 7 промежуточных версий 1 участника)
Строка 8: Строка 8:
  
 
==Формулировка задачи==
 
==Формулировка задачи==
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[[File:2.png]]  
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[[File:7.10.png]]
  
  
−
[[File:1.png]]
+
[[File:7.10(1).png]]
 +
 
 +
==Решение задачи==
 +
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Lebedev/Statika./Polks.html |width=1000 |height=830 |border=0 }}
 +
 
 +
 
 +
<div class="mw-collapsible mw-collapsed" style="width:100%" >
 +
<syntaxhighlight lang="javascript" line start="1" enclose="div">
 +
 
 +
<!DOCTYPE html>
 +
<! не забудьте прописать путь к библиотекам!>
 +
<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>
 +
<div id = "WebGL"> </div>
 +
<div id="Stats-output"></div>
 +
<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';
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this.cos2 = '0';
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this.cos3 = '0';
 +
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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);
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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);
 +
 +
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var res = gui.addFolder('Result');
 +
 
 +
res.add(controls1, 'V').listen();
 +
res.add(controls1, 'cos1').listen();
 +
res.add(controls1, 'cos2').listen();
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res.add(controls1, 'cos3').listen();
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res.add(controls1, 'M').listen();
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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>

Текущая версия на 08:54, 5 февраля 2017

Мещерский Задача 7.10

Визуализация 3D-задачи по статике на JavaScript

Исполнитель: Лебедев Станислав

Группа 23604/1 Кафедра Теоретической механики

Формулировка задачи[править]

7.10.png


7.10(1).png

Решение задачи[править]


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

<!DOCTYPE html> <! не забудьте прописать путь к библиотекам!> <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>
Источник — «http://tm.spbstu.ru/?title=Мещерский_Задача_7.10&oldid=46296»