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Celestial Mechanics and Dynamical Astronomy

, Volume 54, Issue 4, pp 393–399 | Cite as

Kepler's problem in constant curvature spaces

  • Valeri V. Kozlov
  • Alexander O. Harin
Article

Abstract

In this article the generalization of the motion of a particle in a central field to the case of a constant curvature space is investigated. We found out that orbits on a constant curvature surface are closed in two cases: when the potential satisfies Iaplace-Beltrami equation and can be regarded as an analogue 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-centre problem on a constant curvature surface is discovered and it is shown that integrability remains even if elastic “forces” are added.

Key words

Central field closed orbits spheroconical coordinates 

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References

  1. Abdrakhmanov, A.M.: 1990, ‘On Integrable Rebounding Reflection Systems’, Vestn. Mosk. un-ta, Ser. 1, 5, 85–88 (in Russian).Google Scholar
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Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Valeri V. Kozlov
    • 1
  • Alexander O. Harin
    • 1
  1. 1.Dept. of Theoretical MechanicsMoscow State UniversityMoscowU.S.S.R.

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