Celestial Mechanics and Dynamical Astronomy

, Volume 99, Issue 4, pp 253–260 | Cite as

Relations between integrable systems in plane and curved spaces

  • Alexey V. Borisov
  • Ivan S. Mamaev
Original Article


We consider trajectory isomorphisms between various integrable systems on an n-dimensional sphere S n and a Euclidean space \({\mathbb{R}}^n\) . Some of the systems are classical integrable problems of Celestial Mechanics in plane and curved spaces. All the systems under consideration have an additional first integral quadratic in momentum and can be integrated analytically by using the separation of variables. We show that some integrable problems in constant curvature spaces are not essentially new from the viewpoint of the theory of integration, and they can be analyzed using known results of classical Celestial Mechanics.


Integrable systems Euclidean spaces 


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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Institute of Computer ScienceUdmurt State UniversityIzhevskRussia

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