arXiv physics/04020482004-02physics.ed-phphysics.class-ph

一维基本弹性碰撞的台球理论方法

A Billiard-Theoretic Approach to Elementary 1d Elastic Collisions

S. Redner

备注：: 7 pages, 8 figures, 2-column revtex4 format, for submission to the American Journal of Physics. Introductory text, several references and one figure added in response to referee comments. A few more additions and corrections; final version for AJP. Yet a few more changes and one minor error corrected just before publication
发表信息：: Am. J. Phys. 72, 1492-1498 (2004)
DOI：: 10.1119/1.1738428

摘要：

在一维自由运动点粒子的弹性碰撞和相应的台球系统之间建立了一个简单的关系。当两个质量为m_1和m_2的粒子在x>0的半直线上，在x=0时接近弹性势垒时，相应的台球系统是一个无限大的楔形体。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。这种联系很好地解释了“超级球上的一角硬币”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。它还表明，三个弹性粒子在无限线和三个粒子在有限环，分别对应于一个台球在无限楔形和一个三角形台球桌上的运动。它展示了如何根据粒子质量确定这两组的角度。

英文摘要：

A simple relation is developed between elastic collisions of freely-moving point particles in one dimension and a corresponding billiard system. For two particles with masses m_1 and m_2 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 nicely 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 is also 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 on a triangular billiard table. It is shown how to determine the angles of these two sets in terms of the particle masses.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。