Attractive Kepler billiards with focused conic section boundaries

Dekker, Ruben (2026) Attractive Kepler billiards with focused conic section boundaries. Bachelor's Thesis, Mathematics.

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Abstract

Kepler billiards are dynamical systems where a particle orbits around a center of mass, whilst bouncing elastically on a boundary. The original Kepler problem is separable in different coordinate systems. If the boundary is a coordinate line of such a coordinate system, then the Kepler billiards are integrable. In this paper, spherical, elliptical and parabolic coordinates are discussed, resulting in boundaries that are conic sections. Due to the conservation of energy, and the fact that the center of mass does not change over time, we can construct a family of orbits with set constants of motion that orbit around the center of mass. We show in this paper that when a Kepler orbit coincides with a boundary that is a coordinate line of the coordinate system, the new orbit lies in the same family of orbits. In this paper, we study the accessible regions for particles in such systems in two ways; in the classical way, as projection of Liouville tori onto the configuration space, and with a newer method, as envelopes of the respective Kepler family.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Waalkens, H. and Sterk, A.E.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	11 Aug 2026 11:04
Last Modified:	11 Aug 2026 11:04
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/37495

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