Dynamics of a Rotated Orthogonal Gravitational Wedge Billiard

TL;DR

This paper analyzes the dynamics of a rotated orthogonal gravitational wedge billiard, demonstrating its integrability and characterizing periodic orbits, with all other trajectories being dense in the space.

Contribution

It derives conditions for periodic orbits and proves the integrability of the rotated orthogonal gravitational wedge billiard.

Findings

The system is integrable.

Periodic orbits can be explicitly constructed.

Non-periodic trajectories are dense in the configuration space.

Abstract

We investigate a rotated, orthogonal gravitational wedge billiard - a special case of the asymmetric wedge billiard - in which the dynamics are integrable. We derive equations and conditions under which periodic orbits may be constructed for this model, and show that any other trajectory will be dense in the configuration space.