| Текущая версия |
Ваш текст |
| Строка 87: |
Строка 87: |
| | * сброс всех данных до начальных при нажатии кнопки "Reload" | | * сброс всех данных до начальных при нажатии кнопки "Reload" |
| | | | |
| − | {{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Shvarev/4.html |width=1100 |height=500 |border=0 }} | + | {{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Shvarev/4.html |width=1100 |height=600 |border=0 }} |
| − | | |
| − | | |
| − | <div class="mw-collapsible mw-collapsed">
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| − | '''Текст программы на языке JavaScript:''' <div class="mw-collapsible-content">
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| − | Файл '''"4.js"'''
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| − | <syntaxhighlight lang="javascript" line start="1" enclose="div">
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| − | | |
| − | function main()
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| − | {
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| − | var scene = new THREE.Scene();
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| − | var camera = new THREE.PerspectiveCamera(45, window.innerWidth/window.innerHeight, 0.1, 1000);
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| − | var render = new THREE.WebGLRenderer();
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| − | render.setClearColor(0x87CEFA, 1);
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| − | render.setSize(800, 400);
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| − | | |
| − | var axes = new THREE.AxisHelper(20);
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| − | scene.add(axes);
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| − |
| |
| − | /**
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| − | var planeGeometry = new THREE.PlaneGeometry(105,68,50,1);
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| − | */
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| − | var planeGeometry = new THREE.PlaneGeometry(1000,500,50,1);
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| − | var planeMaterial = new THREE.MeshLambertMaterial({color:0x068000});
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| − | var plane = new THREE.Mesh(planeGeometry, planeMaterial);
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| − | plane.position.x=0;
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| − | plane.position.y=0;
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| − | plane.position.z=-0.11;
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| − | | |
| − | scene.add(plane);
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| − |
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| − | var ballGeometry = new THREE.SphereGeometry( 0.11, 16, 16 );
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| − | var ballMaterial = new THREE.MeshBasicMaterial( {color: 0xffff00,wireframe:true} );
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| − | var ball = new THREE.Mesh( ballGeometry, ballMaterial );
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| − | scene.add( ball );
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| − | ball.castShadow = true;
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| − |
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| − |
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| − | var cylinderGeometry = new THREE.CylinderGeometry(0.11,0.11,1,16);
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| − | var cylinderMaterial = new THREE.MeshLambertMaterial({color:0xffff00});
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| − | var cylinder = new THREE.Mesh(cylinderGeometry, cylinderMaterial)
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| − | cylinder.position.x=0;
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| − | cylinder.position.y=0;
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| − | cylinder.position.z=0;
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| − | scene.add(cylinder);
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| − | cylinder.castShadow = true;
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| − |
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| − | var trajectoryGeometryB = new THREE.SphereGeometry(0.05, 16, 16);
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| − | var trajectoryMaterialB = new THREE.MeshBasicMaterial( {color: 0x000000,wireframe:true} );
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| − |
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| − | var trajectoryGeometryC = new THREE.SphereGeometry(0.05, 16, 16);
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| − | var trajectoryMaterialC = new THREE.MeshBasicMaterial( {color: 0xFF0000,wireframe:true} );
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| − |
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| − | var traMaterialB = new THREE.MeshBasicMaterial({color: 0xffffff});
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| − | var traGeometryB = new THREE.CircleGeometry( 0.05, 16);
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| − |
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| − | var traMaterialC = new THREE.MeshBasicMaterial({color: 0xFF9900});
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| − | var traGeometryC = new THREE.CircleGeometry( 0.05, 16);
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| − |
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| − |
| |
| − | /**
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| − | var cubeGeometry = new THREE.CubeGeometry(4,4,4);
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| − | var cubeMesh = new THREE.MeshLambertMaterial({color:0xff0000, wireframe:false});
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| − | var cube = new THREE.Mesh(cubeGeometry, cubeMesh);
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| − | cube.position.x=-4;
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| − | cube.position.y=3;
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| − | cube.position.z=0;
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| − | scene.add(cube);
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| − |
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| − | | |
| − | var cylinderGeometry = new THREE.CylinderGeometry(4,4,5,16);
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| − | var cylinderMaterial = new THREE.MeshLambertMaterial({color:0xaaee00});
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| − | var cylinder = new THREE.Mesh(cylinderGeometry, cylinderMaterial)
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| − | cylinder.position.x=10;
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| − | cylinder.position.y=10;
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| − | cylinder.position.z=0;
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| − |
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| − | scene.add(cylinder);
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| − | */
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| − |
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| − |
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| − |
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| − |
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| − | var spotLight = new THREE.SpotLight(0xffffff);
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| − | spotLight.position.set(0,0,1500);
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| − | scene.add(spotLight);
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| − |
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| − | | |
| − | spotLight.castShadow = true;
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| − | | |
| − |
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| − |
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| − | render.shadowMapEnabled = true;
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| − | plane.receiveShadow = true;
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| − |
| |
| − | /**
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| − | cube.castShadow = true;
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| − | cylinder.castShadow = true;
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| − | */
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| − |
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| − |
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| − |
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| − | var a = new THREE.Vector3( 5, 2, -1 );
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| − | var b = new THREE.Vector3( -1, 1, 1 );
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| − | | |
| − | var c = new THREE.Vector3();
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| − | c.crossVectors( a, b );
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| − |
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| − | camera.position.x= -30;
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| − | camera.position.y= 0;
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| − | camera.position.z= 60;
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| − | camera.lookAt(c);
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| − |
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| − | camera.lookAt(scene.position);
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| − | $("#webGL").append(render.domElement);
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| − |
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| − |
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| − |
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| − | var controls = new function() {
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| − | this.WindPowerX = 0;
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| − | this.WindPowerY = 0;
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| − | this.WindPowerZ = 0;
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| − | this.Mass = 0.45;
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| − | this.Radius = 0.11;
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| − | this.Height = 0.22;
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| − | this.Viscosity = 0.000178;
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| − | this.AirDensity = 1.2754;
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| − | this.g = 9.8
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| − | this.Vx = 15;
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| − | this.Vy = 0;
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| − | this.Vz = 5;
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| − | this.OmegaX = 0;
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| − | this.OmegaY = 0;
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| − | this.OmegaZ = -10;
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| − | }
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| − | var gui = new dat.GUI();
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| − | gui.add(controls, 'WindPowerX',-10,10);
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| − | gui.add(controls, 'WindPowerY',-10,10);
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| − | gui.add(controls, 'WindPowerZ',-10,10);
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| − | gui.add(controls, 'Mass',0.41,0.45);
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| − | gui.add(controls, 'Radius',0.01,0.21);
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| − | gui.add(controls, 'Height',0.1, 1);
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| − | gui.add(controls, 'Viscosity',0.00001, 0.001)
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| − | gui.add(controls, 'AirDensity',1, 1000)
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| − | gui.add(controls, 'g',0, 20)
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| − | gui.add(controls, 'Vx',0,40);
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| − | gui.add(controls, 'Vy',0,40);
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| − | gui.add(controls, 'Vz',0,40);
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| − | gui.add(controls, 'OmegaX',-10,10);
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| − | gui.add(controls, 'OmegaY',-10,10);
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| − | gui.add(controls, 'OmegaZ',-10,10);
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| − |
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| − |
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| − | contr = new THREE.OrbitControls(camera);
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| − | contr.dumping = 0.2;
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| − |
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| − | | |
| − |
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| − | /**contr = new THREE.TrackballControls(camera);
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| − | contr.rotateSpeed = 1.0;
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| − | contr.zoomSpeed = 1.2;
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| − | contr.panSpeed = 0.8;
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| − | contr.noZoom = false;
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| − | contr.noPan = false;
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| − | contr.staticMoving = true;
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| − | contr.dynamicDampingFactor = 0.3;
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| − | contr.keys = [65,83,68];
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| − | */
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| − |
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| − |
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| − | /**window.addEventListener('resize',onWindowResize,false);
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| − | function onWindowResize()
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| − | {
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| − | camera.aspect = window.innerWidth/window.innerHeight;
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| − | camera.updateProjectionMatrix();
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| − | render.setSize(window.innerWidth,window.innerHeight);
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| − |
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| − | renderer();
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| − | }
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| − | */
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| − |
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| − | var stats = initStats();
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| − | var step = 0;
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| − |
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| − |
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| − | Vx = 0;
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| − | Vy = 0;
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| − | Vz = 0;
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| − | Mass = 0;
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| − | Viscosity = 0;
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| − | dt = 0.01;
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| − | Radius = 0;
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| − | g = 0;
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| − | WindX = 0;
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| − | WindY = 0;
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| − | WindZ = 0;
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| − | AirDensity = 0;
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| − |
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| − | Height = 1;
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| − | | |
| − | var VxB =controls.Vx;
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| − | var VxC =controls.Vx;
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| − | var VyB =controls.Vy;
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| − | var VyC =controls.Vy;
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| − | var VzB =controls.Vz;
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| − | var VzC =controls.Vz;
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| − |
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| − | OmegaXB = controls.OmegaX;
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| − | OmegaXC = controls.OmegaX;
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| − | OmegaYB = controls.OmegaY;
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| − | OmegaYC = controls.OmegaY;
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| − | OmegaZB = controls.OmegaZ;
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| − | OmegaZC = controls.OmegaZ;
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| − |
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| − |
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| − | pppB = 0;
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| − | pppC = 0;
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| − | kkk = 0;
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| − |
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| − | function renderer()
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| − | {
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| − | /**
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| − | cube.rotation.x+=controls.rotationSpeed;
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| − | cube.rotation.y+=controls.rotationSpeed;
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| − | cube.rotation.z+=controls.rotationSpeed;
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| − |
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| − | cylinder.position.x = 20+(10*(Math.cos(step)));
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| − | cylinder.position.y = 2+(10*(Math.abs(Math.sin(step))));
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| − |
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| − |
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| − | */
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| − |
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| − | if (pppB == 0)
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| − | {
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| − | VxB+=controls.Vx;
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| − | VyB+=controls.Vy;
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| − | VzB+=controls.Vz;
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| − | WindX = controls.WindPowerX;
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| − | WindY = controls.WindPowerY;
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| − | WindZ = controls.WindPowerZ;
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| − |
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| − | OmegaXB = controls.OmegaX;
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| − | OmegaYB = controls.OmegaY;
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| − | OmegaZB = controls.OmegaZ;
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| − |
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| − |
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| − | pppB = 1;
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| − |
| |
| − | }
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| − |
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| − | UxB = VxB - WindX;
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| − | UyB = VyB - WindY;
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| − | UzB = VzB - WindZ;
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| − | | |
| − | Mass=controls.Mass;
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| − | Radius=controls.Radius;
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| − | Viscosity = controls.Viscosity;
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| − | g = controls.g;
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| − |
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| − | AirDensity = controls.AirDensity;
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| − | | |
| − |
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| − | if (ball.position.z >= 0)
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| − | {
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| − |
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| − | /**
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| − | VxB += (-6*Math.PI*Viscosity*Radius*VxB/Mass + 2*Math.PI*AirDensity*Radius*Radius*Radius*(UyB*OmegaZB - UzB*OmegaYB)/Mass)*dt;
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| − | VyB += (-6*Math.PI*Viscosity*Radius*VyB/Mass + 2*Math.PI*AirDensity*Radius*Radius*Radius*(UzB*OmegaXB - UxB*OmegaZB)/Mass )*dt;
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| − | VzB += (-6*Math.PI*Viscosity*Radius*VzB/Mass - g + 2*Math.PI*AirDensity*Radius*Radius*Radius*(UxB*OmegaYB - UyB*OmegaXB)/Mass)*dt;
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| − |
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| − | OmegaXB += -6*Math.PI*Viscosity*Radius*OmegaXB*Radius/Mass;
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| − | OmegaYB += -6*Math.PI*Viscosity*Radius*OmegaYB*Radius/Mass;
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| − | OmegaZB += -6*Math.PI*Viscosity*Radius*OmegaZB*Radius/Mass;
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| − |
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| − | */
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| − |
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| − | VxB += (2*Math.PI*AirDensity*Radius*Radius*Radius*(UyB*OmegaZB - UzB*OmegaYB)/Mass)*dt;
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| − | VyB += (2*Math.PI*AirDensity*Radius*Radius*Radius*(UzB*OmegaXB - UxB*OmegaZB)/Mass )*dt;
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| − | VzB += (-g + 2*Math.PI*AirDensity*Radius*Radius*Radius*(UxB*OmegaYB - UyB*OmegaXB)/Mass)*dt;
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| − |
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| − | ball.position.x += VxB*dt;
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| − | ball.position.y += VyB*dt;
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| − | ball.position.z += VzB*dt;
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| − |
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| − |
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| − |
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| − | ball.rotation.x += OmegaXB*dt;
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| − | ball.rotation.y += OmegaYB*dt;
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| − | ball.rotation.z += OmegaZB*dt;
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| − |
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| − | var trajectoryB = new THREE.Mesh(trajectoryGeometryB, trajectoryMaterialB);
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| − | trajectoryB.position.x = ball.position.x;
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| − | trajectoryB.position.y = ball.position.y;
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| − | trajectoryB.position.z = ball.position.z;
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| − |
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| − | scene.add( trajectoryB );
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| − |
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| − |
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| − | var traB = new THREE.Mesh( traGeometryB, traMaterialB);
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| − | traB.position.x = ball.position.x;
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| − | traB.position.y = ball.position.y;
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| − | traB.position.z = 0;
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| − | scene.add(traB);
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| − |
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| − | document.getElementById("td1").innerHTML = ball.position.y ;
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| − | document.getElementById("td2").innerHTML = ball.position.x ;
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| − | | |
| − | }
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| − |
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| − | requestAnimationFrame(renderer);
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| − |
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| − | contr.update();
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| − |
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| − | render.render(scene,camera);
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| − |
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| − |
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| − |
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| − |
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| − | }
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| − |
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| − | alpha1 = 0;
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| − | alpha2 = 0;
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| − | alpha3 = 0;
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| − | rot1 = 0;
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| − | rot2 = 0;
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| − | rot3 = 0;
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| − |
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| − | function renderer2()
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| − | {
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| − |
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| − |
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| − | if (pppC == 0)
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| − | {
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| − | VyC+=controls.Vy;
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| − | VxC+=controls.Vx;
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| − | VzC+=controls.Vz;
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| − | WindX = controls.WindPowerX;
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| − | WindY = controls.WindPowerY;
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| − | WindZ = controls.WindPowerZ;
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| − |
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| − | OmegaXC = controls.OmegaX;
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| − | OmegaYC = controls.OmegaY;
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| − | OmegaZC = controls.OmegaZ;
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| − |
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| − |
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| − | pppC = 1;
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| − |
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| − | }
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| − |
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| − | UxC = VxC - WindX;
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| − | UyC = VyC - WindY;
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| − | UzC = VzC - WindZ;
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| − | | |
| − | Mass=controls.Mass;
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| − | Radius=controls.Radius;
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| − | Viscosity = controls.Viscosity;
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| − | g = controls.g;
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| − | Height = controls.Height;
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| − | AirDensity = controls.AirDensity;
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| − |
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| − | var cylinderGeometry = new THREE.CylinderGeometry(2*Radius,2*Radius, Height, 16);
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| − |
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| − | cylinder.geometry = cylinderGeometry;
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| − | | |
| − | | |
| − | if (cylinder.position.z >= 0)
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| − | {
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| − | /**
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| − | VxC += (-6*Math.PI*Viscosity*Radius*VxC/Mass + 2*Math.PI*AirDensity*Radius*Radius*Radius*(UyC*OmegaZC - UzC*OmegaYC)/Mass)*dt;
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| − | VyC += (-6*Math.PI*Viscosity*Radius*VyC/Mass + 2*Math.PI*AirDensity*Radius*Radius*Radius*(UzC*OmegaXC - UxC*OmegaZC)/Mass )*dt;
| |
| − | VzC += (-6*Math.PI*Viscosity*Radius*VzC/Mass - g + 2*Math.PI*AirDensity*Radius*Radius*Radius*(UxC*OmegaYC - UyC*OmegaXC)/Mass)*dt;
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| − |
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| − | OmegaXC += -6*Math.PI*Viscosity*Radius*OmegaXC*Radius/Mass;
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| − | OmegaYC += -6*Math.PI*Viscosity*Radius*OmegaYC*Radius/Mass;
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| − | OmegaZC += -6*Math.PI*Viscosity*Radius*OmegaZC*Radius/Mass;
| |
| − | */
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| − | /**
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| − | VxC += (2*Math.PI*AirDensity*Radius*Radius*Radius*(UyC*OmegaZC - UzC*OmegaYC)/Mass)*dt;
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| − | VyC += (2*Math.PI*AirDensity*Radius*Radius*Radius*(UzC*OmegaXC - UxC*OmegaZC)/Mass )*dt;
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| − | VzC += (-g + 2*Math.PI*AirDensity*Radius*Radius*Radius*(UxC*OmegaYC - UyC*OmegaXC)/Mass)*dt;
| |
| − | */
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| − |
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| − | | |
| − | alpha1 = (cylinder.rotation.x - rot1)/(2*Math.PI);
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| − | alpha2 = (cylinder.rotation.y - rot2)/(2*Math.PI);
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| − | alpha3 = (cylinder.rotation.z - rot3)/(2*Math.PI);
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| − |
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| − | rot1 = cylinder.rotation.x;
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| − | rot2 = cylinder.rotation.y;
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| − | rot3 = cylinder.rotation.z;
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| − |
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| − | VxC += (2*AirDensity*Radius*(2*Radius*Height*Math.cos(alpha1) + Math.PI*Radius*Radius*Math.sin(alpha1) )*(UyC*OmegaZC - UzC*OmegaYC)/Mass)*dt;
| |
| − | VyC += (2*AirDensity*Radius*(2*Radius*Height*Math.sin(alpha2) + Math.PI*Radius*Radius*Math.cos(alpha2))*(UzC*OmegaXC - UxC*OmegaZC)/Mass )*dt;
| |
| − | VzC += (-g + 2*AirDensity*Radius*(2*Radius*Height*Math.cos(alpha3) + Math.PI*Radius*Radius*Math.sin(alpha3))*(UxC*OmegaYC - UyC*OmegaXC)/Mass)*dt;
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| − |
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| − | cylinder.position.x += VxC*dt;
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| − | cylinder.position.y += VyC*dt;
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| − | cylinder.position.z += VzC*dt;
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| − |
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| − | cylinder.rotation.x += OmegaXC*dt;
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| − | cylinder.rotation.y += OmegaYC*dt;
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| − | cylinder.rotation.z += OmegaZC*dt;
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| − |
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| − | | |
| − |
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| − | var trajectoryC = new THREE.Mesh(trajectoryGeometryC, trajectoryMaterialC);
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| − | trajectoryC.position.x = cylinder.position.x;
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| − | trajectoryC.position.y = cylinder.position.y;
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| − | trajectoryC.position.z = cylinder.position.z;
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| − |
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| − | scene.add( trajectoryC );
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| − |
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| − | var traC = new THREE.Mesh( traGeometryC, traMaterialC);
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| − | traC.position.x = cylinder.position.x;
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| − | traC.position.y = cylinder.position.y;
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| − | traC.position.z = 0;
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| − | scene.add(traC);
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| − |
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| − | document.getElementById("td3").innerHTML = cylinder.position.y ;
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| − | document.getElementById("td4").innerHTML = cylinder.position.x;
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| − |
| |
| − | }
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| − |
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| − | requestAnimationFrame(renderer2);
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| − |
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| − | contr.update();
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| − |
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| − | render.render(scene,camera);
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| − |
| |
| − | }
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| − |
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| − | this.start = renderer;
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| − | this.start2 = renderer2;
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| − | | |
| − |
| |
| − |
| |
| − | }
| |
| − | function initStats()
| |
| − | {
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| − | var stats = new Stats();
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| − | stats.setMode(0);
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| − | stats.domElement.style.position='absolute';
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| − | stats.domElement.style.left = '0px';
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| − | stats.domElement.style.top = '0px';
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| − | $("#Stats").append(stats.domElement);
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| − | return stats;
| |
| − | }
| |
| − | | |
| − | | |
| − | | |
| − | </syntaxhighlight>
| |
| − | </div>
| |
| | | | |
| | == Обсуждение результатов и выводы == | | == Обсуждение результатов и выводы == |
| Строка 695: |
Строка 244: |
| | где <math>V_x</math>, <math>V_y</math>, <math>V_z</math> - начальные линейные скорости, <math>ω_x</math>, <math>ω_y</math>, <math>ω_z</math> - начальные угловые скорости, <math>m</math> - масса объекта, <math>r</math> - радиус объекта, <math>h</math> - высота цилиндра, а <math>Δ_y</math> - полученное смещение по оси <math>y</math>. | | где <math>V_x</math>, <math>V_y</math>, <math>V_z</math> - начальные линейные скорости, <math>ω_x</math>, <math>ω_y</math>, <math>ω_z</math> - начальные угловые скорости, <math>m</math> - масса объекта, <math>r</math> - радиус объекта, <math>h</math> - высота цилиндра, а <math>Δ_y</math> - полученное смещение по оси <math>y</math>. |
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| − | '''Вывод:''' Исходя из численных данных, полученных после проведения экспериментов, можно сделать вывод, что относительное смещение зависит от угловой скорости, радиуса, массы и силы тяжести, но не зависит от линейной скорости. Например, при уменьшении угловой скорости в 2 раза следует уменьшение относительного отклонения в ~2 раза, а при уменьшении линейной скорости в 2 раза относительное отклонение остается таким же.
| + | Исходя из числовых данных, полученных после проведения экспериментов, можно сделать вывод, что при большей массе скорость меньше. Это объясняется тем, что на объект большей массы действует большая сила тяжести, препятствующая движению объекта. Также видим, что при уменьшении радиуса смещение уменьшается. Это объясняется тем, что на объект с меньшим радиусом действует меньшая разность давлений при вращении, и, следственно, меньшая сила Магнуса. |
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