Gravitational billiards -- bouncing inside a paraboloid cavity
Dynamical Systems
2023-01-31 v1 Mathematical Physics
Metric Geometry
math.MP
Classical Physics
Abstract
In this work the confined domains for a point-like particle propagating within the boundary of an ideally reflecting paraboloid mirror are derived. Thereby it is proven that all consecutive flight parabola foci points lie on the surface of a common sphere of radius . The main results are illustrated in various limiting cases and are compared to its two-dimensional counterpart.
Keywords
Cite
@article{arxiv.2301.12186,
title = {Gravitational billiards -- bouncing inside a paraboloid cavity},
author = {Daniel Jaud},
journal= {arXiv preprint arXiv:2301.12186},
year = {2023}
}
Comments
12 pages, 7 figures