2D球的碰撞问题：没有能量守恒 [英] 2d Ball Collision Problem: no conservation of energy

问题描述

我试图写一个简单的物理模拟，其中具有不同半径球和群众一个完全弹性和摩擦的环境中跳来跳去。我写我自己code以下这些资源： http://www.vobarian.com/collisions /2dcollisions2.pdf 我还测试了code从这里：的球到球的碰撞 - 检测和处理

I am trying to write a simple physics simulation where balls with varying radii and masses bounce around in a perfectly elastic and frictionless environment. I wrote my own code following this resource: http://www.vobarian.com/collisions/2dcollisions2.pdf and I also tested the code from here: Ball to Ball Collision - Detection and Handling

问题EDITED

随着里克·戈尔茨坦和拉尔夫的帮助下，我已经得到了我的code工作（有一个错字..）。非常感谢您的帮助。不过我仍然困惑，为什么其他的算法是不是为我工作。球在正确的方向上弹开，但该系统的总能量是决不保守的。的速度越来越快，直到球刚开始在屏幕上的静态位置闪烁。其实我是想在我的程序使用此code，因为它是很多比我写的更简洁。

With the help of Rick Goldstein and Ralph, I have gotten my code to work (there was a typo..). Thanks so much for you help. However I am still confused as to why the other algorithm isn't working for me. The balls bounce off in the correct directions, but the total energy of the system is never conserved. The velocities get faster and faster until the balls just start blinking in static positions on the screen. I actually want to use this code in my program, because it is a lot more concise than the one I wrote.

下面是功能性的算法，我写的（虽然我确实需要从其他来源的第一位）。它在泡沫类：

Here is the functional algorithm that I wrote (although I did take the first bit from that other source). Its in a Bubble class:

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);
}

这是一个不正常工作

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));
}

让我知道如果你发现任何东西。谢谢

Let me know if you find anything. Thanks

推荐答案

有在那台v1nPost行一个错字？貌似分母应该是 this.mass + b.mass ，而不是 this.mass * b.mass 。

Is there a typo in the line that sets v1nPost? Looks like the denominator should be this.mass + b.mass, not this.mass * b.mass.

此外，因为你计算这个和 B ，你检查之间的冲突，以确保您又不是也这样做的同一冲突b 和这个，从而加倍三角洲应用到每一个参与泡沫的碰撞？

Also, because you're computing a collision between this and b, are you checking to make sure you're not also doing the same collision between b and this, thus doubling the delta applied to each participating bubble in the collision?

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