Kovalevskaya Top and Generalizations of Integrable Systems
Exactly Solvable and Integrable Systems
2007-05-23 v1
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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Cite
@article{arxiv.nlin/0504002,
title = {Kovalevskaya Top and Generalizations of Integrable Systems},
author = {A. V. Borisov and I. S. Mamaev and A. G. Kholmskaya},
journal= {arXiv preprint arXiv:nlin/0504002},
year = {2007}
}
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21 pages