Kovalevskaya Top and Generalizations of Integrable Systems

Borisov, A. V.; Mamaev, I. S.; Kholmskaya, A. G.

Kovalevskaya Top and Generalizations of Integrable Systems

Authors

Borisov, A. V.

Mamaev, I. S.

Kholmskaya, A. G.

Description

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.
21 pages