Kovalevskaya Top and Generalizations of Integrable Systems

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.

arXiv comment21 pages

Cited by in corpus (4)

• Some Spacetimes with Higher Rank Killing-Stackel Tensors
• Goryachev-Chaplygin, Kovalevskaya, and Brdička-Eardley-Nappi-Witten pp-waves spacetimes with higher rank Stäckel-Killing tensors
• Extensions of the Appelrot classes for the generalized gyrostat in a double force field
• Phase topology of the Kowalevski-Sokolov top