A billiard-theoretic approach to elementary one-dimensional elastic collisions
A billiard-theoretic approach to elementary one-dimensional elastic collisions
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基本一维弹性碰撞的台球理论方法
DOI：
10.1119/1.1738428
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发表时间：
2004
影响因子：
0.9
通讯作者：
S. Redner
中科院分区：
文献类型：
--
作者：
S. Redner
一维自由运动粒子的弹性碰撞与相应的台球系统之间建立了一种简单的关系。对于半线 x>0 上质量为 m1 和 m2 的两个粒子在 x=0 处接近弹性势垒时，相应的台球系统是无限楔形。两个粒子的碰撞历史可以很容易地从相应的台球轨迹中推断出来。这种联系解释了“超级球上的一毛钱”和“篮球上的棒球”的经典演示，这是基础物理课程的主要内容。还表明，无限直线上的三个弹性粒子和有限环上的三个粒子分别对应于无限楔形中和三角形台球桌上的台球的运动。展示了如何根据粒子质量确定这两组的角度。
A simple relation is developed between the elastic collisions of freely moving particles in one dimension and a corresponding billiard system. For two particles with masses m1 and m2 on the half-line x>0 that approach an elastic barrier at x=0, the corresponding billiard system is an infinite wedge. The collision history of the two particles can be easily inferred from the corresponding billiard trajectory. This connection explains the classic demonstrations of the “dime on the superball” and the “baseball on the basketball” that are a staple in elementary physics courses. It also is shown that three elastic particles on an infinite line and three particles on a finite ring correspond, respectively, to the motion of a billiard ball in an infinite wedge and on a triangular billiard table. It is shown how to determine the angles of these two sets in terms of the particle masses.