A classification of classical billiard trajectories

TL;DR

This paper classifies the different types of classical billiard trajectories within a rectangular well, identifying periodic, open, and special pocketed paths using Hamilton-Jacobi analysis.

Contribution

It provides a systematic classification of billiard trajectories in a rectangular well, highlighting the conditions for each trajectory type.

Findings

Identification of three main trajectory types: periodic, open, and pocketed.

Use of Hamilton-Jacobi equation to analyze classical particle motion.

Characterization of special trajectories when particles are pocketed.

Abstract

We examine the possible trajectories of a classical particle, trapped in a two-dimensional infinite rectangular well, using the Hamilton-Jacobi equation. We observe that three types of trajectories are possible: periodic orbits, open orbits and some special trajectories when the particle gets pocketed.