Superintegrable systems on a sphere

    2005, Volume 10, Number 3, pp.  257-266

    Author(s): Borisov A. V., Mamaev I. S.

    We consider various generalizations of the Kepler problem to three-dimensional sphere $S^3$, (a compact space of constant curvature). In particular, these generalizations include addition of a spherical analogue of the magnetic monopole (the Poincaré–Appell system) and addition of a more complicated field which is a generalization of the MICZ-system. The mentioned systems are integrable superintegrable, and there exists the vector integral which is analogous to the Laplace–Runge–Lenz vector. We offer a classification of the motions and consider a trajectory isomorphism between planar and spatial motions. The presented results can be easily extended to Lobachevsky space $L^3$.
    Keywords: spaces of constant curvature, Kepler problem, integrability
    Citation: Borisov A. V., Mamaev I. S., Superintegrable systems on a sphere , Regular and Chaotic Dynamics, 2005, Volume 10, Number 3, pp. 257-266

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