This article is cited in 11 papers

Kovalevskaya Top and Generalizations of Integrable Systems

A. V. Borisov^a, I. S. Mamaev^b, A. G. Kholmskaya<sup>c

a</sup> Department of Theoretical Mechanics, Moscow State University, Vorob'ievy Gory, 119899, Moscow, Russia
^b Laboratory of Dynamical Chaos and Nonlinearity, Udmurt State University, Universitetskaya, 1, 426034, Izhevsk, Russia
^c Udmurt State University, Universitetskaya, 1, 426034, Izhevsk, Russia

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.

MSC: 70E17, 70G40

Received: 12.12.2000

Language: English

DOI: 10.1070/RD2001v006n01ABEH000161

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