Kepler's problem in constant curvature spaces

Details Kepler's problem in constant curvature spaces Kepler's problem in constant curvature spaces

Dec 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992cemda..54..393k&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 54, no. 4, p. 393-399.

Mathematics

Dynamical Systems

27

Gravitational Effects, Gravitational Fields, Kepler Laws, Laplace Equation, Particle Motion, Celestial Mechanics, Dynamical Systems, Gravitational Constant

Scientific paper

The generalization of the motion of a particle in a central field to the case of a constant curvature space is investigated. We found that orbits on a constant curvature surface are closed in two cases: when the potential satisfies Laplace-Beltrami equation and can be regarded as an analog of the potential of the gravitational interaction, and in the case when the potential is the generalization of the potential of an elastic spring. Also, the full integrability of the generalized two-center problem on a constant curvature surface is discovered and it is shown that integrability remains even if elastic 'forces' are added.

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