Система блоков — различия между версиями

Материал из Department of Theoretical and Applied Mechanics
Перейти к: навигация, поиск
(→‎Решение частного случая)
 
(не показано 27 промежуточных версий 2 участников)
Строка 1: Строка 1:
 
'''''Задача:''''' С помощью языка программирования JavaScript смоделировать систему блоков с грузом.
 
'''''Задача:''''' С помощью языка программирования JavaScript смоделировать систему блоков с грузом.
−
[[Файл:Blocks.png|thumb|Система блоков с грузом (1 - подвижный блок, 2 - неподвижный блок, 3 - груз.]]
+
[[Файл:Blocks.png|thumb|Система блоков с грузом (1 - подвижный блок, 2 - неподвижный блок, 3 - груз.)]]
 +
 
 +
== Решение ==
 +
 
 +
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Shvarev/5.html |width=800 |height=600 |border=0 }}
 +
 
 +
Программа: [[Медиа: Blocks.zip|скачать]]
 +
 
 +
<div class="mw-collapsible mw-collapsed">
 +
'''Текст программы на языке JavaScript:''' <div class="mw-collapsible-content">
 +
Файл '''"5.js"'''
 +
<syntaxhighlight lang="javascript" line start="1" enclose="div">
 +
function main()
 +
{
 +
var scene = new THREE.Scene();
 +
var camera = new THREE.PerspectiveCamera(45, window.innerWidth/window.innerHeight, 0.1, 1000);
 +
var render = new THREE.WebGLRenderer();
 +
render.setClearColor(0xEEEEEE, 1);
 +
render.setSize(window.innerWidth, window.innerHeight);
 +
 +
 +
var axes = new THREE.AxisHelper(20);
 +
scene.add(axes);
 +
 +
 +
var planeGeometry = new THREE.PlaneGeometry(60,40,50,1);
 +
var planeMaterial = new THREE.MeshLambertMaterial({color:0x6699FF});
 +
var plane = new THREE.Mesh(planeGeometry, planeMaterial);
 +
plane.rotation.x = -0.5*Math.PI;
 +
plane.position.x=15;
 +
plane.position.y=0;
 +
plane.position.z=14;
 +
scene.add(plane);
 +
 +
 +
var planeGeometry = new THREE.PlaneGeometry(20,60,50,1);
 +
var planeMaterial = new THREE.MeshLambertMaterial({color:0xffffff});
 +
var plane1 = new THREE.Mesh(planeGeometry, planeMaterial);
 +
plane1.rotation.z = -0.5*Math.PI;
 +
plane1.position.x=15;
 +
plane1.position.y=10;
 +
plane1.position.z=-6;
 +
scene.add(plane1);
 +
 +
 +
var boxGeometry1 = new THREE.BoxGeometry(0.1,4,16);
 +
var boxMaterial1 = new THREE.MeshLambertMaterial({color:0xE5DD06, wireframe:false});
 +
var cube1 = new THREE.Mesh(boxGeometry1, boxMaterial1);
 +
cube1.position.x=8;
 +
cube1.position.y=10;
 +
cube1.position.z=2;
 +
scene.add(cube1);
 +
 +
var boxGeometry2 = new THREE.BoxGeometry(0.1,4,10);
 +
var boxMaterial2 = new THREE.MeshLambertMaterial({color:0xE5DD06, wireframe:false});
 +
var cube2 = new THREE.Mesh(boxGeometry2, boxMaterial2);
 +
cube2.position.x=16;
 +
cube2.position.y=10;
 +
cube2.position.z=5;
 +
scene.add(cube2);
 +
 +
var boxGeometry3 = new THREE.BoxGeometry(0.1,4,8);
 +
var boxMaterial3 = new THREE.MeshLambertMaterial({color:0xE5DD06, wireframe:false});
 +
var cube3 = new THREE.Mesh(boxGeometry3, boxMaterial3);
 +
cube3.position.x=24;
 +
cube3.position.y=10;
 +
cube3.position.z=4;
 +
scene.add(cube3);
 +
 +
 +
 +
 +
/**
 +
var cubeGeometry = new THREE.CubeGeometry(4,4,4);
 +
var cubeMesh = new THREE.MeshLambertMaterial({color:0xff0000, wireframe:false});
 +
var cube = new THREE.Mesh(cubeGeometry, cubeMesh);
 +
cube.position.x=-4;
 +
cube.position.y=3;
 +
cube.position.z=0;
 +
scene.add(cube);
 +
 +
 
 +
var cylinderGeometry = new THREE.CylinderGeometry(4,4,5,16);
 +
var cylinderMaterial = new THREE.MeshLambertMaterial({color:0xaaee00});
 +
var cylinder = new THREE.Mesh(cylinderGeometry, cylinderMaterial)
 +
cylinder.position.x=10;
 +
cylinder.position.y=10;
 +
cylinder.position.z=0;
 +
 +
scene.add(cylinder);
 +
*/
 +
 +
 +
var cylinderGeometry = new THREE.CylinderGeometry(4,4,4,32);
 +
var cylinderMaterial = new THREE.MeshLambertMaterial({color:0xff0000, wireframe: false});
 +
 +
var cylinder1 = new THREE.Mesh(cylinderGeometry, cylinderMaterial)
 +
cylinder1.position.x=12;
 +
cylinder1.position.y=10;
 +
cylinder1.position.z=10;
 +
scene.add(cylinder1);
 +
 +
var cylinder2 = new THREE.Mesh(cylinderGeometry, cylinderMaterial)
 +
cylinder2.position.x=20;
 +
cylinder2.position.y=10;
 +
cylinder2.position.z=0;
 +
scene.add(cylinder2);
 +
 +
var semiCylinderGeometry1 = new THREE.CylinderGeometry(4,4,4,32, 1,true, -Math.PI/2, Math.PI);
 +
var semiCylinderGeometry2 = new THREE.CylinderGeometry(4,4,4,32, 1,true, Math.PI/2, Math.PI);
 +
var semiCylinderMaterial = new THREE.MeshLambertMaterial({color:0xE5DD06, wireframe: false});
 +
var semiCylinder1 = new THREE.Mesh(semiCylinderGeometry1, semiCylinderMaterial)
 +
var semiCylinder2 = new THREE.Mesh(semiCylinderGeometry2, semiCylinderMaterial)
 +
 +
semiCylinder1.position.x=12;
 +
semiCylinder1.position.y=10;
 +
semiCylinder1.position.z=10;
 +
scene.add(semiCylinder1);
 +
 +
semiCylinder2.position.x=20;
 +
semiCylinder2.position.y=10;
 +
semiCylinder2.position.z=0;
 +
scene.add(semiCylinder2);
 +
 +
 +
var pyrGeometry = new THREE.CylinderGeometry(4,4,4,3);
 +
var pyrMaterial = new THREE.MeshLambertMaterial({color:0xff8800, wireframe:false});
 +
var pyr = new THREE.Mesh(pyrGeometry, pyrMaterial)
 +
pyr.position.x=20;
 +
pyr.position.y=10;
 +
pyr.position.z=-4;
 +
scene.add(pyr);
 +
 +
 +
var cubeGeometry = new THREE.CubeGeometry(4,4,2);
 +
var cubeMesh = new THREE.MeshLambertMaterial({color:0xff0000, wireframe:false});
 +
var cube = new THREE.Mesh(cubeGeometry, cubeMesh);
 +
cube.position.x=24;
 +
cube.position.y=10;
 +
cube.position.z=9;
 +
scene.add(cube);
 +
 +
 +
/**
 +
var line_geometry = new THREE.Geometry();
 +
line_geometry.vertices.push(new THREE.Vector3(16,10,0));
 +
    line_geometry.vertices.push(new THREE.Vector3(16,10,10));
 +
var  material_line = new THREE.LineBasicMaterial({ color: 0x6699FF, linewidth: 5000, fog:false});
 +
var line1 = new THREE.Line(line_geometry,material_line);
 +
    scene.add( line1);
 +
 
 +
 +
var line_geometry = new THREE.Geometry();
 +
    line_geometry.vertices.push(new THREE.Vector3(8,10,10));
 +
    line_geometry.vertices.push(new THREE.Vector3(8,10,-6));
 +
var  material_line = new THREE.LineBasicMaterial({ color: 0x6699FF, linewidth: 5000, fog:false});
 +
var line2 = new THREE.Line(line_geometry,material_line);
 +
    scene.add(line2);
 +
 
 +
var line_geometry = new THREE.Geometry();
 +
    line_geometry.vertices.push(new THREE.Vector3(24,10,0));
 +
    line_geometry.vertices.push(new THREE.Vector3(24,10,8));
 +
var  material_line = new THREE.LineBasicMaterial({ color: 0x6699FF, linewidth: 5000, fog:false});
 +
var line3 = new THREE.Line(line_geometry,material_line);
 +
    scene.add(line3);
 +
 
 +
*/
 +
 +
var  spotLight = new THREE.SpotLight(0xffffff);
 +
spotLight.position.set(0,100,0);
 +
scene.add(spotLight);
 +
 +
var  spotLight1 = new THREE.SpotLight(0xffffff);
 +
spotLight1.position.set(50,100,30);
 +
scene.add(spotLight1);
 +
 +
 +
 +
render.shadowMapEnabled = true;
 +
plane.receiveShadow = true;
 +
 +
/**
 +
cube.castShadow = true;
 +
cylinder.castShadow = true;
 +
*/
 +
spotLight.castShadow = true;
 +
 
 +
 +
 +
 +
 +
camera.position.x= 0;
 +
camera.position.y= 100;
 +
camera.position.z= 0;
 +
camera.lookAt(scene.position);
 +
$("#webGL").append(render.domElement);
 +
 +
 +
 +
var controls = new function() {
 +
this.bouncingSpeed = 0.03;
 +
this.r1 = 2;
 +
}
 +
var gui = new dat.GUI();
 +
gui.add(controls, 'bouncingSpeed',0,0.5);
 +
gui.add(controls, 'r1',1,2.5);
 +
 +
contr = new THREE.OrbitControls(camera);
 +
contr.dumping = 0.2;
 +
 +
 
 +
 +
/**contr = new THREE.TrackballControls(camera);
 +
contr.rotateSpeed = 1.0;
 +
contr.zoomSpeed = 1.2;
 +
contr.panSpeed = 0.8;
 +
contr.noZoom = false;
 +
contr.noPan = false;
 +
contr.staticMoving = true;
 +
contr.dynamicDampingFactor = 0.3;
 +
contr.keys = [65,83,68];
 +
*/
 +
 +
 +
window.addEventListener('resize',onWindowResize,false);
 +
function onWindowResize()
 +
{
 +
camera.aspect = window.innerWidth/window.innerHeight;
 +
camera.updateProjectionMatrix();
 +
render.setSize(window.innerWidth,window.innerHeight);
 +
 +
renderer();
 +
}
 +
 +
var stats = initStats();
 +
var step = 0;
 +
 +
var z1 =16;
 +
var z2 = 10;
 +
var z3 = 8;
 +
 +
var r2 = 2;
 +
 
 +
var r1 = 2;
 +
 +
 +
function renderer()
 +
{
 +
/**
 +
cube.rotation.x+=controls.rotationSpeed;
 +
cube.rotation.y+=controls.rotationSpeed;
 +
cube.rotation.z+=controls.rotationSpeed;
 +
 +
cylinder.position.x = 20+(10*(Math.cos(step)));
 +
cylinder.position.y = 2+(10*(Math.abs(Math.sin(step))));
 +
 +
 +
*/
 +
 +
 +
step+=controls.bouncingSpeed;
 +
step1 = step/100;
 +
step2 = step/200;
 +
 
 +
r1 = controls.r1;
 +
r2 = 4 - r1;
 +
 +
var geometryCylinder2 = new THREE.CylinderGeometry(2*r1,2*r1,4,32);
 +
var geometryCylinder1 = new THREE.CylinderGeometry(2*r2,2*r2,4,32);
 +
 +
cylinder2.geometry = geometryCylinder2;
 +
cylinder1.geometry = geometryCylinder1;
 +
 +
 +
 +
var semiGeometryCylinder2 = new THREE.CylinderGeometry(2*r1,2*r1,4,32, 1,true, Math.PI/2, Math.PI);
 +
var semiGeometryCylinder1 = new THREE.CylinderGeometry(2*r2,2*r2,4,32, 1,true, -Math.PI/2, Math.PI);
 +
 +
semiCylinder2.geometry = semiGeometryCylinder2;
 +
semiCylinder1.geometry = semiGeometryCylinder1;
 +
 +
 +
z1 -=step2;
 +
z2 -=step2;
 +
z3 +=step1;
 +
var geometry1 = new THREE.BoxGeometry( 0.01, 4, z1 );
 +
var geometry2 = new THREE.BoxGeometry( 0.01, 4, z2 );
 +
var geometry3 = new THREE.BoxGeometry( 0.01, 4, z3 );
 +
cube1.position.x =12 - 2*r2;
 +
cube2.position.x = 12 + 2*r2;
 +
cube3.position.x = 20 + 2*r1;
 +
if ( cube2.position.z >= cylinder2.position.z)
 +
{
 +
 +
 
 +
 +
cube1.geometry = geometry1;
 +
cube1.position.z -= step2/2;
 +
 +
 +
 +
cube2.geometry = geometry2;
 +
cube2.position.z -= step2/2;
 +
 +
cube3.geometry = geometry3;
 +
cube3.position.z += step1/2;
 +
 +
 +
 +
cylinder1.rotation.y+=step2/2;
 +
cylinder2.rotation.y-=step1/2;
 +
 +
 +
 +
/**
 +
line3.geometry.vertices[1].z += step1 ;
 +
line3.geometry.verticesNeedUpdate = true;
 +
 +
line2.geometry.vertices[0].z -= step2 ;
 +
 
 +
line2.geometry.verticesNeedUpdate = true;
 +
 +
 +
line1.geometry.vertices[1].z -= step2 ;
 +
line1.geometry.verticesNeedUpdate = true;
 +
 +
*/
 +
 +
cylinder1.position.z -= step2;
 +
 +
 +
 +
 +
 +
semiCylinder1.position.z -=step2;
 +
 +
cube.position.z += step1;
 +
}
 +
 +
 +
document.getElementById("td1").innerHTML = cube2.position.z ;
 +
 +
requestAnimationFrame(renderer);
 +
 +
contr.update();
 +
 +
render.render(scene,camera);
 +
 +
 +
 +
 +
}
 +
this.start = renderer;
 +
 +
 +
}
 +
function initStats()
 +
{
 +
var stats = new Stats();
 +
stats.setMode(0);
 +
stats.domElement.style.position='absolute';
 +
stats.domElement.style.left = '0px';
 +
stats.domElement.style.top = '0px';
 +
$("#Stats").append(stats.domElement);
 +
return stats;
 +
}
 +
 
 +
 
 +
</syntaxhighlight>
 +
</div>
  
 
== Используемые библиотеки ==
 
== Используемые библиотеки ==
  
 +
* cloudflare.js
 +
* dat.gui.js
 +
* googleapis.js
 +
* orbitControls.js
 +
* stats.js
 +
* trackballControls.js
  
 
== Возможности программы ==
 
== Возможности программы ==
  
 +
* задание радиусов блоков
 +
* задание скорости вращения блоков
 +
* запуск программы по кнопке
 +
* получение координаты груза
  
 
== Решение частного случая ==
 
== Решение частного случая ==
 +
 +
'''''Условия задачи:'''''
 +
[[Файл:Blocks2.png|thumb|Картинка к задаче.]]
 +
Подвижный блок <math>1</math> и неподвижный блок <math>2</math> соединены нерастяжимой нитью. Груз <math>K</math>, прикрепленный к концу этой нити, опускается по закону <math> x = 2t^2 </math> м. Определить скорости точек <math>C, D,B</math> и <math>E</math>, лежащих на ободе подвижного блока, в момент времени <math>t = 1</math> с. в положении, указанном на рисунке, если радиус подвижного блока <math>1</math> равен <math>0.2</math> м., а <math>CD\perp BE</math>. Найти также угловую скорость блока <math>1</math>.
 +
 +
'''''Решение:'''''
 +
 +
<math>C</math> - мгновенный центр скоростей, <math>v_{C} = 0</math>;
 +
 +
<math>v_{K} = v_{D} = \dot{x} = 4</math> м/c;
 +
 +
<math>ω = \frac{v_{D}}{DC} = \frac{4}{0.4} = 10 c^{-1} </math>;
 +
 +
<math> v_{O} = ω*r = 10*0.2 = 2</math> м/c.
 +
 +
== См. также ==
 +
 +
* [[Справка:Содержание|Справочная информация]]
 +
* [[Проектная деятельность по информатике]]
 +
 +
 +
[[Category: Студенческие проекты]]

Текущая версия на 13:26, 19 мая 2015

Задача: С помощью языка программирования JavaScript смоделировать систему блоков с грузом.

Система блоков с грузом (1 - подвижный блок, 2 - неподвижный блок, 3 - груз.)

Решение[править]

Программа: скачать

Текст программы на языке JavaScript:

Файл "5.js" 

  1 function main()
  2 {
  3 	var scene = new THREE.Scene();
  4 	var camera = new THREE.PerspectiveCamera(45, window.innerWidth/window.innerHeight, 0.1, 1000);
  5 	var render = new THREE.WebGLRenderer();
  6 	render.setClearColor(0xEEEEEE, 1);
  7 	render.setSize(window.innerWidth, window.innerHeight);
  8 	
  9 	
 10 	var axes = new THREE.AxisHelper(20);
 11 	scene.add(axes);
 12 	
 13 	
 14 	var planeGeometry = new THREE.PlaneGeometry(60,40,50,1);
 15 	var planeMaterial = new THREE.MeshLambertMaterial({color:0x6699FF});
 16 	var plane = new THREE.Mesh(planeGeometry, planeMaterial);
 17 	plane.rotation.x = -0.5*Math.PI;
 18 	plane.position.x=15;
 19 	plane.position.y=0;
 20 	plane.position.z=14;
 21 	scene.add(plane);
 22 	
 23 	
 24 	var planeGeometry = new THREE.PlaneGeometry(20,60,50,1);
 25 	var planeMaterial = new THREE.MeshLambertMaterial({color:0xffffff});
 26 	var plane1 = new THREE.Mesh(planeGeometry, planeMaterial);
 27 	plane1.rotation.z = -0.5*Math.PI;
 28 	plane1.position.x=15;
 29 	plane1.position.y=10;
 30 	plane1.position.z=-6;
 31 	scene.add(plane1);
 32 	
 33 	
 34 	var boxGeometry1 = new THREE.BoxGeometry(0.1,4,16);
 35 	var boxMaterial1 = new THREE.MeshLambertMaterial({color:0xE5DD06, wireframe:false});
 36 	var cube1 = new THREE.Mesh(boxGeometry1, boxMaterial1);
 37 	cube1.position.x=8;
 38 	cube1.position.y=10;
 39 	cube1.position.z=2;
 40 	scene.add(cube1);
 41 	
 42 	var boxGeometry2 = new THREE.BoxGeometry(0.1,4,10);
 43 	var boxMaterial2 = new THREE.MeshLambertMaterial({color:0xE5DD06, wireframe:false});
 44 	var cube2 = new THREE.Mesh(boxGeometry2, boxMaterial2);
 45 	cube2.position.x=16;
 46 	cube2.position.y=10;
 47 	cube2.position.z=5;
 48 	scene.add(cube2);
 49 	
 50 	var boxGeometry3 = new THREE.BoxGeometry(0.1,4,8);
 51 	var boxMaterial3 = new THREE.MeshLambertMaterial({color:0xE5DD06, wireframe:false});
 52 	var cube3 = new THREE.Mesh(boxGeometry3, boxMaterial3);
 53 	cube3.position.x=24;
 54 	cube3.position.y=10;
 55 	cube3.position.z=4;
 56 	scene.add(cube3);
 57 	
 58 	
 59 	
 60 	
 61 	/**
 62 	var cubeGeometry = new THREE.CubeGeometry(4,4,4);
 63 	var cubeMesh = new THREE.MeshLambertMaterial({color:0xff0000, wireframe:false});
 64 	var cube = new THREE.Mesh(cubeGeometry, cubeMesh);
 65 	cube.position.x=-4;
 66 	cube.position.y=3;
 67 	cube.position.z=0;
 68 	scene.add(cube);
 69 	
 70 
 71 	var cylinderGeometry = new THREE.CylinderGeometry(4,4,5,16);
 72 	var cylinderMaterial = new THREE.MeshLambertMaterial({color:0xaaee00});
 73 	var cylinder = new THREE.Mesh(cylinderGeometry, cylinderMaterial)
 74 	cylinder.position.x=10;
 75 	cylinder.position.y=10;
 76 	cylinder.position.z=0;
 77 	
 78 	scene.add(cylinder);
 79 	*/
 80 	
 81 	
 82 	var cylinderGeometry = new THREE.CylinderGeometry(4,4,4,32);
 83 	var cylinderMaterial = new THREE.MeshLambertMaterial({color:0xff0000, wireframe: false});
 84 	
 85 	var cylinder1 = new THREE.Mesh(cylinderGeometry, cylinderMaterial)
 86 	cylinder1.position.x=12;
 87 	cylinder1.position.y=10;
 88 	cylinder1.position.z=10;
 89 	scene.add(cylinder1);
 90 	
 91 	var cylinder2 = new THREE.Mesh(cylinderGeometry, cylinderMaterial)
 92 	cylinder2.position.x=20;
 93 	cylinder2.position.y=10;
 94 	cylinder2.position.z=0;
 95 	scene.add(cylinder2);
 96 	
 97 	var semiCylinderGeometry1 = new THREE.CylinderGeometry(4,4,4,32, 1,true, -Math.PI/2, Math.PI);
 98 	var semiCylinderGeometry2 = new THREE.CylinderGeometry(4,4,4,32, 1,true, Math.PI/2, Math.PI);
 99 	var semiCylinderMaterial = new THREE.MeshLambertMaterial({color:0xE5DD06, wireframe: false});
100 	var semiCylinder1 = new THREE.Mesh(semiCylinderGeometry1, semiCylinderMaterial)
101 	var semiCylinder2 = new THREE.Mesh(semiCylinderGeometry2, semiCylinderMaterial)
102 	
103 	semiCylinder1.position.x=12;
104 	semiCylinder1.position.y=10;
105 	semiCylinder1.position.z=10;
106 	scene.add(semiCylinder1);
107 	
108 	semiCylinder2.position.x=20;
109 	semiCylinder2.position.y=10;
110 	semiCylinder2.position.z=0;
111 	scene.add(semiCylinder2);
112 	
113 	
114 	var pyrGeometry = new THREE.CylinderGeometry(4,4,4,3);
115 	var pyrMaterial = new THREE.MeshLambertMaterial({color:0xff8800, wireframe:false});
116 	var pyr = new THREE.Mesh(pyrGeometry, pyrMaterial)
117 	pyr.position.x=20;
118 	pyr.position.y=10;
119 	pyr.position.z=-4;
120 	scene.add(pyr);
121 	
122 	
123 	var cubeGeometry = new THREE.CubeGeometry(4,4,2);
124 	var cubeMesh = new THREE.MeshLambertMaterial({color:0xff0000, wireframe:false});
125 	var cube = new THREE.Mesh(cubeGeometry, cubeMesh);
126 	cube.position.x=24;
127 	cube.position.y=10;
128 	cube.position.z=9;
129 	scene.add(cube);
130 	
131 	
132 	/**
133 	var line_geometry = new THREE.Geometry();
134 	line_geometry.vertices.push(new THREE.Vector3(16,10,0));
135     line_geometry.vertices.push(new THREE.Vector3(16,10,10));
136 	var   material_line = new THREE.LineBasicMaterial({ color: 0x6699FF, linewidth: 5000, fog:false});
137 	var line1 = new THREE.Line(line_geometry,material_line);	
138     scene.add( line1);
139 
140 		
141 	var line_geometry = new THREE.Geometry();
142     line_geometry.vertices.push(new THREE.Vector3(8,10,10));
143     line_geometry.vertices.push(new THREE.Vector3(8,10,-6));
144 	var   material_line = new THREE.LineBasicMaterial({ color: 0x6699FF, linewidth: 5000, fog:false});
145 	var line2 = new THREE.Line(line_geometry,material_line);	
146     scene.add(line2);
147 
148 	var line_geometry = new THREE.Geometry();
149     line_geometry.vertices.push(new THREE.Vector3(24,10,0));
150     line_geometry.vertices.push(new THREE.Vector3(24,10,8));
151 	var   material_line = new THREE.LineBasicMaterial({ color: 0x6699FF, linewidth: 5000, fog:false});
152 	var line3 = new THREE.Line(line_geometry,material_line);	
153     scene.add(line3);
154 
155 	*/
156 	
157 	var  spotLight = new THREE.SpotLight(0xffffff);
158 	spotLight.position.set(0,100,0);
159 	scene.add(spotLight);
160 	
161 	var  spotLight1 = new THREE.SpotLight(0xffffff);
162 	spotLight1.position.set(50,100,30);
163 	scene.add(spotLight1);
164 	
165 	
166 	
167 	render.shadowMapEnabled = true;
168 	plane.receiveShadow = true;
169 	
170 	/**
171 	cube.castShadow = true;
172 	cylinder.castShadow = true;
173 	*/
174 	spotLight.castShadow = true;
175 
176 	
177 	
178 	
179 	
180 	camera.position.x= 0;
181 	camera.position.y= 100;
182 	camera.position.z= 0;
183 	camera.lookAt(scene.position);
184 	$("#webGL").append(render.domElement);
185 	
186 	
187 	
188 	var controls = new function() {
189 		this.bouncingSpeed = 0.03;
190 		this.r1 = 2;
191 	}
192 	var gui = new dat.GUI();
193 	gui.add(controls, 'bouncingSpeed',0,0.5);
194 	gui.add(controls, 'r1',1,2.5);
195 		
196 	contr = new THREE.OrbitControls(camera);
197 	contr.dumping = 0.2;
198 	
199 
200 	
201 	/**contr = new THREE.TrackballControls(camera);
202 	contr.rotateSpeed = 1.0;
203 	contr.zoomSpeed = 1.2;
204 	contr.panSpeed = 0.8;
205 	contr.noZoom = false;
206 	contr.noPan = false;
207 	contr.staticMoving = true;
208 	contr.dynamicDampingFactor = 0.3;
209 	contr.keys = [65,83,68];
210 	*/
211 	
212 	
213 	window.addEventListener('resize',onWindowResize,false);
214 	function onWindowResize()
215 	{
216 		camera.aspect = window.innerWidth/window.innerHeight;
217 		camera.updateProjectionMatrix();
218 		render.setSize(window.innerWidth,window.innerHeight);
219 	
220 		renderer();
221 	}
222 	
223 	var stats = initStats();
224 	var step = 0;
225 	
226 	var z1 =16;
227 	var z2 = 10;
228 	var z3 = 8;
229 	
230 	var r2 = 2;
231 
232 	var r1 = 2;
233 	
234 	
235 	function renderer()
236 	{
237 		/**
238 		cube.rotation.x+=controls.rotationSpeed;
239 		cube.rotation.y+=controls.rotationSpeed;
240 		cube.rotation.z+=controls.rotationSpeed;
241 		
242 		cylinder.position.x = 20+(10*(Math.cos(step)));
243 		cylinder.position.y = 2+(10*(Math.abs(Math.sin(step))));
244 		
245 		
246 		*/
247 		
248 		
249 		step+=controls.bouncingSpeed;
250 		step1 = step/100;
251 		step2 = step/200;
252 
253 		r1 = controls.r1;
254 		r2 = 4 - r1;
255 		
256 		var geometryCylinder2 = new THREE.CylinderGeometry(2*r1,2*r1,4,32);
257 		var geometryCylinder1 = new THREE.CylinderGeometry(2*r2,2*r2,4,32);
258 	
259 		cylinder2.geometry = geometryCylinder2;
260 		cylinder1.geometry = geometryCylinder1;
261 		
262 		
263 		
264 		var semiGeometryCylinder2 = new THREE.CylinderGeometry(2*r1,2*r1,4,32, 1,true, Math.PI/2, Math.PI);
265 		var semiGeometryCylinder1 = new THREE.CylinderGeometry(2*r2,2*r2,4,32, 1,true, -Math.PI/2, Math.PI);
266 	
267 		semiCylinder2.geometry = semiGeometryCylinder2;
268 		semiCylinder1.geometry = semiGeometryCylinder1;
269 		
270 		
271 		z1 -=step2;
272 		z2 -=step2;
273 		z3 +=step1;
274 		var geometry1 = new THREE.BoxGeometry( 0.01, 4, z1 );
275 		var geometry2 = new THREE.BoxGeometry( 0.01, 4, z2 );
276 		var geometry3 = new THREE.BoxGeometry( 0.01, 4, z3 );
277 		cube1.position.x =12 - 2*r2;
278 		cube2.position.x = 12 + 2*r2;
279 		cube3.position.x = 20 + 2*r1;
280 		if ( cube2.position.z >= cylinder2.position.z)
281 		{	
282 		
283 
284 		
285 		cube1.geometry = geometry1;
286 		cube1.position.z -= step2/2;
287 		
288 		
289 		
290 		cube2.geometry = geometry2;
291 		cube2.position.z -= step2/2;
292 		
293 		cube3.geometry = geometry3;
294 		cube3.position.z += step1/2;
295 		
296 				
297 			
298 		cylinder1.rotation.y+=step2/2;
299 		cylinder2.rotation.y-=step1/2;
300 		
301 		
302 		
303 		/**
304 		line3.geometry.vertices[1].z += step1 ;
305 		line3.geometry.verticesNeedUpdate = true;
306 		
307 		line2.geometry.vertices[0].z -= step2 ;
308 
309 		line2.geometry.verticesNeedUpdate = true;
310 		
311 		
312 		line1.geometry.vertices[1].z -= step2 ;
313 		line1.geometry.verticesNeedUpdate = true;
314 		
315 		*/
316 		
317 		cylinder1.position.z -= step2; 
318 		
319 		
320 		
321 		
322 		
323 		semiCylinder1.position.z -=step2;
324 		
325 		cube.position.z += step1;
326 		}
327 		
328 			
329 		document.getElementById("td1").innerHTML = cube2.position.z ;
330 		
331 		requestAnimationFrame(renderer);
332 		
333 		contr.update();
334 		
335 		render.render(scene,camera);
336 		
337 		
338 		
339 		
340 	}
341 	this.start = renderer;
342 	
343 	
344 }
345 function initStats()
346 {
347 	var stats = new Stats();
348 	stats.setMode(0);
349 	stats.domElement.style.position='absolute';
350 	stats.domElement.style.left = '0px';
351 	stats.domElement.style.top = '0px';
352 	$("#Stats").append(stats.domElement);
353 	return stats;
354 }

Используемые библиотеки[править]

  • cloudflare.js
  • dat.gui.js
  • googleapis.js
  • orbitControls.js
  • stats.js
  • trackballControls.js

Возможности программы[править]

  • задание радиусов блоков
  • задание скорости вращения блоков
  • запуск программы по кнопке
  • получение координаты груза

Решение частного случая[править]

Условия задачи:

Картинка к задаче.

Подвижный блок [math]1[/math] и неподвижный блок [math]2[/math] соединены нерастяжимой нитью. Груз [math]K[/math], прикрепленный к концу этой нити, опускается по закону [math] x = 2t^2 [/math] м. Определить скорости точек [math]C, D,B[/math] и [math]E[/math], лежащих на ободе подвижного блока, в момент времени [math]t = 1[/math] с. в положении, указанном на рисунке, если радиус подвижного блока [math]1[/math] равен [math]0.2[/math] м., а [math]CD\perp BE[/math]. Найти также угловую скорость блока [math]1[/math].

Решение:

[math]C[/math] - мгновенный центр скоростей, [math]v_{C} = 0[/math];

[math]v_{K} = v_{D} = \dot{x} = 4[/math] м/c;

[math]ω = \frac{v_{D}}{DC} = \frac{4}{0.4} = 10 c^{-1} [/math];

[math] v_{O} = ω*r = 10*0.2 = 2[/math] м/c.

См. также[править]

Источник — «http://tm.spbstu.ru/?title=Система_блоков&oldid=33730»