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

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

2009-05-31

arxiv.org/abs/0906.0174v1

Physics

Mathematical Physics

Scientific paper

10.1016/j.jde.2009.05.003

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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