JavaScript投げ上げたボールの反射

JavaScriptです。

投げ上げた物体が自由落下して床面で弾む
様子をシミュレーションするスクリプトを作成したいです。．
three.jsでしてます。

発生している問題・エラーメッセージ

球を投げ上げてからそのまま落下してしまいます。
投げ上げ→落下→弾みにしたいです。
今は投げ上げ→落下のままなので弾みを加えたいです。

x＿ｋ（ｙ座標）がもし負になるようだったら速度を反転する
的なものを追加すると思うのですが…

JavaScript
1．<!DOCTYPE html>
2
3<html>
4
5<head>
6    <title>Sample5_3</title>
7    <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/three.js/r121/three.js"></script>
8    <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/stats.js/r16/Stats.js"></script>
9    <script type="text/javascript" src="https://cdn.jsdelivr.net/npm/three@0.101.1/examples/js/controls/OrbitControls.js"></script>
10    <script src="myMatrix.js"></script>
11    <style>
12        body {
13            /* set margin to 0 and overflow to hidden, to go fullscreen */
14            margin: 0;
15            overflow: hidden;
16        }
17    </style>
18</head>
19<body>
20
21<div id="Stats-output">
22</div>
23<!-- Div which will hold the Output -->
24<div id="WebGL-output">
25</div>
26
27<!-- Javascript code that runs our Three.js examples -->
28<script type="text/javascript">
29
30    // once everything is loaded, we run our Three.js stuff.
31    function init() {
32
33        var  dt = 1/60, //サンプリングタイム
34            x_k = [[0], [10]]; //xの初期値
35
36        var stats = initStats();
37
38        // create a scene, that will hold all our elements such as objects, cameras and lights.
39        var scene = new THREE.Scene();
40
41        // create a camera, which defines where we're looking at.
42        var camera = new THREE.PerspectiveCamera(45, window.innerWidth / window.innerHeight, 0.1, 1000);
43
44        const controls = new THREE.OrbitControls(camera);
45
46        // create a render and set the size
47        var renderer = new THREE.WebGLRenderer();
48
49        renderer.setClearColor(new THREE.Color(0xEEEEEE));
50        renderer.setSize(window.innerWidth, window.innerHeight);
51        renderer.shadowMap.enabled = true;
52
53        // create the ground plane
54        var planeGeometry = new THREE.PlaneGeometry(2, 2, 1, 1);
55        var planeMaterial = new THREE.MeshLambertMaterial({color: 0xffffff, side: THREE.DoubleSide});
56        var plane = new THREE.Mesh(planeGeometry, planeMaterial);
57        plane.receiveShadow = true;
58
59        // rotate and position the plane
60        plane.rotation.x = -0.5 * Math.PI;
61        plane.position.x = 0;
62        plane.position.y = 0;
63        plane.position.z = 0;
64
65        // add the plane to the scene
66        scene.add(plane);
67
68        // create the sphere
69        var sphereGeometry = new THREE.SphereGeometry(0.1, 20, 20);
70        var sphereMaterial = new THREE.MeshLambertMaterial({color: 0x777777});
71        var sphere = new THREE.Mesh(sphereGeometry, sphereMaterial);
72
73        // position the sphere
74        sphere.position.x = 0;
75        sphere.position.y = 0;
76        sphere.position.z = 0;
77        sphere.castShadow = true;
78
79        scene.add(sphere);
80
81        // position and point the camera to the center of the scene
82        camera.position.x = -6;
83        camera.position.y = 3;
84        camera.position.z = 6;
85        camera.lookAt(scene.position);
86
87        // add subtle ambient lighting
88        var ambientLight = new THREE.AmbientLight(0x0c0c0c);
89        scene.add(ambientLight);
90
91        // add spotlight for the shadows
92        var spotLight = new THREE.SpotLight(0xffffff);
93        spotLight.position.set(-2, 3, -0.5);
94        spotLight.castShadow = true;
95        scene.add(spotLight);
96
97        // add the output of the renderer to the html element
98        document.getElementById("WebGL-output").appendChild(renderer.domElement);
99
100        // call the render function
101        renderScene();
102
103      function renderScene() {
104          stats.update();
105
106          sphere.position.y = x_k[0][0]+ 0.1/2;
107
108          x_k = runge_kutta(x_k);
109          
110
111          
112
113
114          // render using requestAnimationFrame
115          requestAnimationFrame(renderScene);
116          renderer.render(scene, camera);
117        }
118
119        function initStats() {
120          var stats = new Stats();
121          stats.setMode(0); // 0: fps, 1: ms
122          // Align top-left
123          stats.domElement.style.position = 'absolute';
124          stats.domElement.style.left = '0px';
125          stats.domElement.style.top = '0px';
126          document.getElementById("Stats-output").appendChild(stats.domElement);
127          return stats;
128        }
129
130       function runge_kutta(x_k) {
131          var k1  = scalar_matrix(dt, func(x_k));
132          var k2  = scalar_matrix(dt, func(add_matrix(x_k, scalar_matrix(1/2, k1))));
133          var k3  = scalar_matrix(dt, func(add_matrix(x_k, scalar_matrix(1/2, k2))));
134          var k4  = scalar_matrix(dt, func(add_matrix(x_k, k3)));
135          var x_k1 = add_matrix(x_k, scalar_matrix(1/6, add_matrix(add_matrix(k1, scalar_matrix(2, k2)), add_matrix(scalar_matrix(2, k3), k4))));
136          return x_k1;
137        }
138
139        //導関数
140        function func(x) {
141          var M = 0.5,
142          C = 0.2,
143          f = [[0], [0]];
144          f[0][0] = x[1][0];
145          f[1][0] = -9.8 - C/M*x[1][0];
146          return f;
147        }
148
149    }
150    window.onload = init;
151</script>
152</body>
153</html>