Kovalevskaya top and generalizations of integrable systems

    2001, Volume 6, Number 1, pp.  1-16

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

    Generalizations of the Kovalevskaya, Chaplygin, Goryachev–Chaplygin and Bogoyavlensky systems on a bundle are considered in this paper. Moreover, a method of introduction of separating variables and action-angle variables is described. Another integration method for the Kovalevskaya top on the bundle is found. This method uses a coordinate transformation that reduces the Kovalevskaya system to the Neumann system. The Kolosov analogy is considered. A generalization of a recent Gaffet system to the bundle of Poisson brackets is obtained at the end of the paper.
    Citation: Borisov A. V., Mamaev I. S., Kholmskaya A. G., Kovalevskaya top and generalizations of integrable systems, Regular and Chaotic Dynamics, 2001, Volume 6, Number 1, pp. 1-16

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