Elastic interactions in physics are reflections in geometry

Abstract

A simple standard problem in physics is the study of elastic collisions between elements of an ideal system, which consists of two point masses and a wall. Based on energy and momentum conservation laws, solving the problem consists in finding the intersection of a straight line with a conic. Relationships between the solutions are easily obtained if we consider the right (fundamental) basis to express the solutions. The geometric interpretation follows easily: moving from one point to another on a conic using directions given by this basis. With simple changes in variables, reflections and rotations appear clearly. Similarities with other phenomena such as Heron’s reflection principle in optics and Kepler’s second law of planetary motion are pointed out.