My final project for the Computational Physics course is a simulator of a Dynamic Billiard system. Billiards are dynamic energy-conserving systems characterized by the Hamiltonian:

where p, q are the canonical coordinates of the particle. The potential V(q) takes the form:

where capital Omega marks the region defined by the confines of the billiard table.

Like the popular game, particles in a dynamic billiard are subjected to movement on a geodesic line and reflections
from the boundary.

The study of dynamic billiards offers a simple and elegant way of studying integrability and chaotic motion, as well as fundamental concepts of cluster physics - Boltzman's ergodic hypothesis for example.

The project explores the behaviour of particles on a 2D composite table:

The left part of the table is characterized by two parameters - the length of the table and the squared ratio between the length and the width. The right table is also characterized by two parameters - length and width. The parameters are chosen such that the right table enforces a periodic motion - by ensuring a rational ratio between length and width. The left table allows an ergodic motion, by allowing a non-rational ratio between the edges.

Download and installation notes can be found here

Guide to the use of the simulator can be found here