Редактирование: Задача Д.24, вариант 20 из Задачника Яблонского

== Условие задачи==
Определить частоты малых свободных колебаний и формы главных колебаний системы с двумя степенями свободы, пренебрегая силами сопротивления, массами пружин и моментами инерции скручиваемых валов.

<math>m_1=8 кг;</math>
<math>m_2=10 кг;</math>
<math>c_1=40  Н⁄см;</math>
<math>c_2=60  Н⁄см;</math>
<math>l=0,5 м</math>

== Программа ==

{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/KaloevaDiana/D24_20/Project.html |width=1200 |height=800 |border=0 }}

== Код программы ==
<div class="mw-collapsible mw-collapsed">
'''Текст программы:''' <div class="mw-collapsible-content">
<syntaxhighlight lang="javascript" line start="1" enclose="div">
    const scene = new THREE.Scene();
    const camera = new THREE.PerspectiveCamera(60, 1, 1, 100);
    const renderer = new THREE.WebGLRenderer();

    //Постановка задачи(условия)
    const R = 2;
    const solution = new function () {
        this.c1 = 20000;
        this.c2 = 30000;
        this.c3 = 10000;
        this.R = .2;
        this.t = 0;
        this.dt = .7;

        this.m1 = 50;
        this.m2 = 60;
        this.m3 = 40;
        this.m4 = 50;


        this.a11 = .5*(this.m1+this.m2)*Math.pow(this.R,2);
        this.a22 = .5*(this.m3+this.m4)*Math.pow(this.R,2);
        this.c11 = this.c1+this.c2/1.44;
        this.c22 = this.c2/.81 + this.c3;
        this.c12 = this.c2/(1.2*.9);
        this.D = Math.sqrt(Math.pow(this.a11 * this.c22 + this.a22 * this.c11,2) -4 * this.a11 * this.a22 * (this.c11 * this.c22 - Math.pow(this.c12,2)));
        this.k1 = '' + Math.sqrt((this.a11 * this.c22 + this.a22 * this.c11 + this.D)/(2*this.a11*this.a22));
        this.k2 = '' + Math.sqrt((this.a11 * this.c22 + this.a22 * this.c11 - this.D)/(2*this.a11*this.a22));

        this.p1 = -(this.c11 - this.a11*Math.pow(this.k1,2))/this.c12;
        this.p2 = -(this.c11 - this.a11*Math.pow(this.k2,2))/this.c12;

        let self = this;

        this.redraw = function() {
            self.t = 0;
            ctx.clearRect(0,-242,500,500);
            ctx1.clearRect(0,-242,500,500);
        };
    };
    class Construction {
        constructor(geometry,material,x,y,z) {
            this.geometry = geometry;
            this.material = material;
            this.x = x;
            this.y = y;
            this.z = z;
            this.mesh = new THREE.Mesh(geometry,material);
        }
        build(scene,angleX,angleY,angleZ) {
            this.mesh.position.x = this.x;
            this.mesh.position.y = this.y;
            this.mesh.position.z = this.z;
            this.mesh.rotation.x = angleX;
            this.mesh.rotation.y = angleY;
            this.mesh.rotation.z = angleZ;
            scene.add(this.mesh);
        }
    }

    class Moving_parts extends Construction {
        spin(solution,sign,ratio,r) {
            let r1 = 1;
            let r2 = 1;
            if(r !== 1) {
                r1 =  solution.p1;
                r2 =  solution.p2;
            }
            this.mesh.rotation.x = r1 * sign * Math.sin(solution.k1 * solution.t / 1000) * 2 / ratio + r2 * sign * Math.sin(solution.k2 * solution.t / 1000) * 2 / ratio;
        }
        static equation(solution,sign,ratio,r,t) {
            let r1 = 1;
            let r2 = 1;
            if(r !== 1) {
                r1 =  solution.p1;
                r2 =  solution.p2;
            }
            return r1 * sign * Math.sin(solution.k1 * t / 1000) * 50 / ratio + r2 * sign * Math.sin(solution.k2 * t / 1000) * 50 / ratio;
        }
    }


    renderer.setClearColor(0xEEEEEE);
    renderer.setSize(600, 600);
    let main = document.getElementById("canvas_3d");
    main.appendChild(renderer.domElement);
    renderer.domElement.style.border = "1px solid#000";


    let gr = new GraphicBulider(450,242);
    let ctx = gr.dom("canvas_1");
    let gr1 = new GraphicBulider(450,242);
    let ctx1 = gr1.dom("canvas_2");
    let buffer = GraphicBulider.createBuffer();
    let buffer1 = GraphicBulider.createBuffer();


    const spotLight = new THREE.SpotLight( 0xffffff );
    spotLight.position.set( 50, 80, 20 );
    scene.add(spotLight);

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

    //Условия задачи
    let wall_1 = new Construction(new THREE.CubeGeometry(10,5,1),new THREE.MeshLambertMaterial({color: 0xff0000,wireframe: false}),0,0,0);
    let shaft_1 = new Construction(new THREE.CylinderGeometry(.5,.5,10,20,10),new THREE.MeshLambertMaterial({color: 0xff0000,wireframe: false}),5.5,0,0);
    let wheel_1 = new Moving_parts(new THREE.CylinderGeometry(2*R,2*R,1,20,5),new THREE.MeshLambertMaterial({color: 0xff0000,wireframe: true}),11,0,0);
    let wheel_2 = new Moving_parts(new THREE.CylinderGeometry(2*R*1.2,2*R*1.2,1,20,5),new THREE.MeshLambertMaterial({color: 0xff0000,wireframe: true}),11,-(2*R+1.2*R*2),0);
    let shaft_2 = new Construction(new THREE.CylinderGeometry(.5,.5,10,20,10),new THREE.MeshLambertMaterial({color: 0xff0000,wireframe: false}),16.5,-(2*R+1.2*R*2),0);
    let wheel_3 = new Moving_parts(new THREE.CylinderGeometry(2*R*.9,2*R*.9,1,20,5),new THREE.MeshLambertMaterial({color: 0xff0000,wireframe: true}),22,-(2*R+1.2*R*2),0);
    let wheel_4 = new Moving_parts(new THREE.CylinderGeometry(2*R,2*R,1,20,5),new THREE.MeshLambertMaterial({color: 0xff0000,wireframe: true}),22,-(2*R+1.2*R*2+.9*R*2+2*R),0);
    let shaft_3 = new Construction(new THREE.CylinderGeometry(.5,.5,5,20,10),new THREE.MeshLambertMaterial({color: 0xff0000,wireframe: false}),19,-(2*R+1.2*R*2+.9*R*2+2*R),0);
    let wall_2 = new Construction(new THREE.CubeGeometry(10,5,1),new THREE.MeshLambertMaterial({color: 0xff0000,wireframe: false}),17,-(2*R+1.2*R*2+.9*R*2+2*R),0);
    wall_1.build(scene,0,Math.PI/2,0);
    shaft_1.build(scene,0,0,Math.PI/2);
    wheel_1.build(scene,0,0,Math.PI/2);
    wheel_2.build(scene,0,0,Math.PI/2);
    shaft_2.build(scene,0,0,Math.PI/2);
    wheel_3.build(scene,0,0,Math.PI/2);
    wheel_4.build(scene,0,0,Math.PI/2);
    shaft_3.build(scene,0,0,Math.PI/2);
    wall_2.build(scene,0,Math.PI/2,0);

    camera.position.x = 20;
    camera.position.y = 10;
    camera.position.z = 40;
    camera.lookAt(scene.position);
    scene.rotation.y = -.5;
    scene.position.y = 8.5;

    let T = solution.dt;
    let z =.001;
    let animate;
    animate = function () {
        requestAnimationFrame(animate);

        T = solution.dt;
        solution.a11 = .5 * (solution.m1 + solution.m2) * Math.pow(solution.R, 2);
        solution.a22 = .5 * (solution.m3 + solution.m4) * Math.pow(solution.R, 2);
        solution.c11 = solution.c1 + solution.c2 / 1.44;
        solution.c22 = solution.c2 / .81 + solution.c3;
        solution.c12 = (1 / (1.2 * .9)) * solution.c2;
        solution.D = Math.sqrt(Math.pow(solution.a11 * solution.c22 + solution.a22 * solution.c11, 2) - 4 * solution.a11 * solution.a22 * (solution.c11 * solution.c22 - Math.pow(solution.c12, 2)));
        solution.k1 = '' + Math.sqrt((solution.a11 * solution.c22 + solution.a22 * solution.c11 + solution.D) / (2 * solution.a11 * solution.a22));
        solution.k2 = '' + Math.sqrt((solution.a11 * solution.c22 + solution.a22 * solution.c11 - solution.D) / (2 * solution.a11 * solution.a22));
        solution.p1 = -(solution.c11 - solution.a11 * Math.pow(solution.k1, 2)) / solution.c12;
        solution.p2 = -(solution.c11 - solution.a11 * Math.pow(solution.k2, 2)) / solution.c12;


        wheel_1.spin(solution, 1, 1, 1);
        wheel_2.spin(solution, -1, 1.2, 1);
        wheel_3.spin(solution, -1, .9, 2);
        wheel_4.spin(solution, 1, 1, 2);

        if (solution.t === 0) {
            z = 0;
        }
        if (solution.t > 450) {
            z -= T;
        }
        ctx.clearRect(0, 0, buffer.width, 400);
        ctx.drawImage(GraphicBulider.bufferDraw(buffer, solution.t, T, Moving_parts.equation(solution, 1, 1, 1, solution.t - T), Moving_parts.equation(solution, 1, 1, 1, solution.t), 'red'), z, 0);
        ctx1.clearRect(0, 0, buffer.width, 400);
        ctx1.drawImage(GraphicBulider.bufferDraw(buffer1, solution.t, T, Moving_parts.equation(solution, 1, 1, 0, solution.t - T), Moving_parts.equation(solution, 1, 1, 0, solution.t), 'green'), z, 0);
        solution.t += T;
        renderer.render(scene, camera);
    };
    animate();
    const gui = new dat.GUI();
    gui.add(solution, 'm1',20,70).onChange(solution.redraw);
    gui.add(solution, 'm2',20,70).onChange(solution.redraw);
    gui.add(solution, 'm3',20,70).onChange(solution.redraw);
    gui.add(solution, 'm4',20,70).onChange(solution.redraw);
    gui.add(solution, 'c1',0,35000).onChange(solution.redraw);
    gui.add(solution, 'c2',0,35000).onChange(solution.redraw);
    gui.add(solution, 'dt',0,10).onChange(solution.redraw);

    gui.add(solution, 'k1').listen();
    gui.add(solution, 'k2').listen();
    gui.add(solution, 'redraw');
    solution.redraw();
</syntaxhighlight>
</div>

== Используемые библиотеки ==

* three.js
* jquery-1.9.0.js
* stats.js
* dat.gui.js
* OrbitControls.js

== Скачать работу ==

* [http://mech.spbstu.ru/File:KR_PL_2018_KaloevaDE.docx  Скачать текст работы].
* [http://mech.spbstu.ru/File:D24_20.rar  Скачать программу].