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arXiv · 0906.0174

Block regularization of the Kepler problem on surfaces of revolution with positive constant curvature

Manuele Santoprete
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Abstract

We consider the Kepler problem on surfaces of revolution that are homeomorphic to $S^2$ and have constant Gaussian curvature. We show that the system is maximally superintegrable, finding constants of motion that generalize the Runge-Lentz vector. Then, using such first integrals, we determine the class of surfaces that lead to block-regularizable collision singularities. In particular we show that the singularities are always regularizable if the surfaces are spherical orbifolds of revolution with constant curvature.

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Manuele Santoprete. 2009-05-31. Block regularization of the Kepler problem on surfaces of revolution with positive constant curvature. https://doi.org/10.1016/j.jde.2009.05.003

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