2d球碰撞问题:没有能量守恒

Question

我正在尝试编写一个简单的物理模拟,其中具有不同半径和质量的球在完全弹性和无摩擦的环境中反弹.我按照以下资源编写了自己的代码:http://www.vobarian.com/collisions/2dcollisions2.pdf,我也从这里测试了代码:Ball to Ball Collision - 检测和处理

编辑问题

在Rick Goldstein和Ralph的帮助下,我得到了我的代码(有一个错字......).非常感谢你的帮助.但是我仍然感到困惑,为什么其他算法不适合我.球以正确的方向反弹,但系统的总能量永远不会被保存.速度变得越来越快,直到球刚刚开始在屏幕上的静态位置闪烁.我实际上想在我的程序中使用这个代码,因为它比我编写的代码简洁得多.

这是我写的功能算法(尽管我从其他来源获取了第一位).它在泡泡类中:

public void resolveCollision(Bubble b)
{
    // get the minimum translation distance
    Vector2 delta = (position.subtract(b.position));
    float d = delta.getMagnitude();
    // minimum translation distance to push balls apart after intersecting
    Vector2 mtd = delta.multiply(((getRadius() + b.getRadius())-d)/d); 

    // resolve intersection --
    // inverse mass quantities
    float im1 = 1 / getMass(); 
    float im2 = 1 / b.getMass();

    // push-pull them apart based off their mass
    position = position.add(mtd.multiply(im1 / (im1 + im2)));
    b.position = b.position.subtract(mtd.multiply(im2 / (im1 + im2)));

    //get the unit normal and unit tanget vectors
    Vector2 uN = b.position.subtract(this.position).normalize();
    Vector2 uT = new Vector2(-uN.Y, uN.X);

    //project ball 1 & 2 's velocities onto the collision axis
    float v1n = uN.dot(this.velocity);
    float v1t = uT.dot(this.velocity);
    float v2n = uN.dot(b.velocity);
    float v2t = uT.dot(b.velocity);

    //calculate the post collision normal velocities (tangent velocities don't change)
    float v1nPost = (v1n*(this.mass-b.mass) + 2*b.mass*v2n)/(this.mass+b.mass);
    float v2nPost = (v2n*(b.mass-this.mass) + 2*this.mass*v1n)/(this.mass+b.mass);

    //convert scalar velocities to vectors
    Vector2 postV1N = uN.multiply(v1nPost);
    Vector2 postV1T = uT.multiply(v1t);
    Vector2 postV2N = uN.multiply(v2nPost);
    Vector2 postV2T = uT.multiply(v2t);

    //change the balls velocities
    this.velocity = postV1N.add(postV1T);
    b.velocity = postV2N.add(postV2T);
}

这是一个不起作用的

public void resolveCollision(Bubble b)
{
    // get the minimum translation distance
    Vector2 delta = (position.subtract(b.position));
    float d = delta.getMagnitude();
    // minimum translation distance to push balls apart after intersecting
    Vector2 mtd = delta.multiply(((getRadius() + b.getRadius())-d)/d); 

    // resolve intersection --
    // inverse mass quantities
    float im1 = 1 / getMass(); 
    float im2 = 1 / b.getMass();

    // push-pull them apart based off their mass
    position = position.add(mtd.multiply(im1 / (im1 + im2)));
    b.position = b.position.subtract(mtd.multiply(im2 / (im1 + im2)));

    // impact speed
    Vector2 v = (this.velocity.subtract(b.velocity));
    float vn = v.dot(mtd.normalize());

    // sphere intersecting but moving away from each other already
    if (vn > 0.0f) return;

    // collision impulse (1f is the coefficient of restitution)
    float i = (-(1.0f + 1f) * vn) / (im1 + im2);
    Vector2 impulse = mtd.multiply(i);

    // change in momentum
    this.velocity = this.velocity.add(impulse.multiply(im1));
    b.velocity = b.velocity.subtract(impulse.multiply(im2));
}

如果你发现任何事情,请告诉我.谢谢

Answer 1

设置v1nPost的行中是否有拼写错误？看起来分母应该是this.mass + b.mass,而不是this.mass * b.mass.

此外,因为你计算之间的碰撞this和b,你检查,以确保你不是也做的同样的碰撞b和this,从而加倍三角洲应用于碰撞每个参与泡沫？