球与球碰撞 - 碰撞时获得显着的速度

Question

我在Objective-C中实现了" Ball to Ball Collision - Detection and Handling " 问题的代码.然而,每当球以一定角度碰撞时,它们的速度会急剧增加.所有的矢量数学都是使用cocos2d-iphone完成的,标题为CGPointExtension.h.这种不希望的加速的原因是什么？

以下是速度提高的示例:

输入:
质量== 12.56637
velocity.x == 1.73199439
velocity.y == -10.5695238

ball.mass == 12.56637
ball.velocity.x == 6.04341078
ball.velocity.y == 14.2686739

输出:
质量== 12.56637
velocity.x == 110.004326
velocity.y == -10.5695238

ball.mass == 12.56637
ball.velocity.x == -102.22892
ball.velocity.y == -72.4030228

#import "CGPointExtension.h"
#define RESTITUTION_CONSTANT (0.75) //elasticity of the system

- (void) resolveCollision:(Ball*) ball
{
    // get the mtd (minimum translation distance)
    CGPoint delta = ccpSub(position, ball.position);
    float d = ccpLength(delta);
    // minimum translation distance to push balls apart after intersecting
    CGPoint mtd = ccpMult(delta, (((radius + ball.radius)-d)/d)); 


    // resolve intersection --
    // inverse mass quantities
    float im1 = 1 / [self mass]; 
    float im2 = 1 / [ball mass];

    // push-pull them apart based off their mass
    position = ccpAdd(position, ccpMult(mtd, (im1 / (im1 + im2))));
    ball.position = ccpSub(ball.position, ccpMult(mtd, (im2 / (im1 + im2))));

    // impact speed
    CGPoint v = ccpSub(velocity, ball.velocity);
    float vn = ccpDot(v,ccpNormalize(mtd));

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

    // collision impulse
    float i = (-(1.0f + RESTITUTION_CONSTANT) * vn) / ([self mass] + [ball mass]);
    CGPoint impulse = ccpMult(mtd, i);


    // change in momentum
    velocity = ccpAdd(velocity, ccpMult(impulse, im1));
    ball.velocity = ccpSub(ball.velocity, ccpMult(impulse, im2));

}

Answer 1

通过原始海报审查了原始代码和注释后,代码看起来是一样的,所以如果原始代码是正确的实现,我会怀疑一个坏的矢量库或某种未初始化的变量.

为什么要在恢复系数上加1.0？

来自:http://en.wikipedia.org/wiki/Coefficient_of_restitution

COR通常是[0,1]范围内的数字.定性地,1表示完全弹性碰撞,而0表示完全非弹性碰撞.大于1的COR在理论上是可能的,表示产生动能的碰撞,例如地雷被抛在一起并爆炸.

另一个问题是:

/ (im1 + im2)

你用除了质量的倒数之和来得到沿着接触向量的冲动 - 你可能应该除以质量本身的总和.这是放大你的冲动("这就是她所说的").