Computational Study of the Dynamics of an Asymmetric Wedge Billiard

Author:

Anderson Keegan D.1ORCID,Villet Charles M.1

Affiliation:

1. Department of Mathematics and Applied Mathematics, University of Johannesburg, Auckland Park, Johannesburg, Gauteng 2092, South Africa

Abstract

We introduce the asymmetric wedge billiard as a generalization of the wedge billiard first studied by Lehtihet and Miller in 1986. This is a billiard system in which the billiard ball moves under the influence of a constant gravitational field, colliding elastically with two wedge walls with the collisions obeying the reflection law. Collision maps are given from which derivatives and area-preservation (or lack thereof) were determined. Expressions for the fixed points of the collision maps were also calculated and discussed. Long-term dynamics were determined computationally from which we observed integrable, quasi-periodic and chaotic behavior which were all dependent on the wedge angles.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Confocal parabolic billiard with gravitational potential: Classical and quantum description;Communications in Nonlinear Science and Numerical Simulation;2024-11

2. One-Dimensional Relativistic Self-Gravitating Systems;Entropy;2024-07-21

3. Dynamics of a Rotated Orthogonal Gravitational Wedge Billiard;International Journal of Bifurcation and Chaos;2023-09-30

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