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arXiv · 1411.7068

On the trajectories of O(1)-Kepler Problems

Guowu Meng
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Abstract

The trajectories of the $\mathrm{O}(1)$-Kepler problem at level $n\ge 2$ are completely determined. It is found in particular that a non-colliding trajectory is an ellipse, a parabola or a branch of hyperbola according as the total energy is negative, zero or positive. Moreover, it is shown that the group $\mathrm{GL}(n, \mathbb R)/\mathrm{O}(1)$ acts transitively on both the set of oriented elliptic trajectories and the set of oriented parabolic trajectories. The method employed here is similar to the one used by Levi-Civita in the study of planar Kepler problem in 1920.

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Guowu Meng. 2015-06-23. On the trajectories of O(1)-Kepler Problems. https://doi.org/10.1063/1.4921244

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