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arXiv · 2301.12186

Gravitational billiards -- bouncing inside a paraboloid cavity

Daniel Jaud
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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 $R$. The main results are illustrated in various limiting cases and are compared to its two-dimensional counterpart.

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Daniel Jaud. 2023-01-28. Gravitational billiards -- bouncing inside a paraboloid cavity. https://doi.org/10.13140/rg.2.2.15184.58888

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