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Kovalevskaya Top and Generalizations of Integrable Systems

A. V. Borisov·I. S. Mamaev·A. G. Kholmskaya
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Abstract

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.

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A. V. Borisov, I. S. Mamaev, A. G. Kholmskaya. 2005-04-01. Kovalevskaya Top and Generalizations of Integrable Systems. https://arxiv.org/abs/nlin/0504002

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