Kepler motion on single-sheet hyperboloid
Yu.A. Kurochkin, V.S. Otchik, L.G. Mardoyan, D.R. Petrosyan, G.S., Pogosyan
TL;DR
This paper solves the Kepler-Coulomb problem on a single-sheet hyperboloid using Hamilton-Jacobi theory, showing all bounded orbits are closed and periodic, with paths forming ellipses or circles.
Contribution
It provides an exact solution for the Kepler problem on hyperbolic geometry and characterizes the nature of bounded orbits in this setting.
Findings
All bounded orbits are closed and periodic.
Paths are ellipses or circles for finite motion.
The problem is solved within the Hamilton-Jacobi framework.
Abstract
The classical Kepler-Coulomb problem on the single-sheeted hyperboloid is solved in the framework of the Hamilton--Jacobi equation. We have proven that all the bounded orbits are closed and periodic. The paths are ellipses or circles for finite motion.
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