Gravitational billiards -- bouncing inside a paraboloid cavity
arXiv:2301.12186 · doi:10.13140/RG.2.2.15184.58888
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.
12 pages, 7 figures