A Graphical User Interface to Simulate Classical Billiard Systems

TL;DR

This paper introduces a Matlab-based GUI tool for simulating classical billiard systems, aiding research and education by visualizing fundamental physical phenomena in simple geometries.

Contribution

It provides a user-friendly Matlab module for simulating billiard tables with line segments and elliptical arcs, enhancing accessibility for research and teaching.

Findings

Efficient simulation of simple billiard tables

Limited reliability for complex boundary components

Accessible tool for educational and research purposes

Abstract

Classical billiards constitute an important class of dynamical systems. They have not only been in used in mathematical disciplines such as ergodic theory, but their properties demonstrate fundamental physical phenomena that can be observed in laboratory settings. This document provides instructions for a Matlab module that simulates classical billiard systems. It is intended to be used as both a research and teaching tool. At present, the program efficiently simulates tables that are constructed entirely from line segments and elliptical arcs. It functions less reliably for tables with more complex boundary components. The program and documentation can be downloaded from \textit{http://www.math.gatech.edu/$\sim$mason/papers/}.