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New families of conservative systems on $S^2$ possessing an integral of fourth degree in momenta

Elena N. Selivanova
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Abstract

There is a well-known example of integrable conservative system on $S^2$, the case of Kovalevskaya in the dynamics of a rigid body, possessing an integral of fourth degree in momenta. Goryachev proposed a one-parameter family of examples of conservative systems on $S^2$ possessing an integral of fourth degree in momenta which includes the case of Kovalevskaya. In this paper we proposed new examples of conservative systems on $S^2$ possessing an integral of fourth degree in momenta.

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BibTeXRIS

Elena N. Selivanova. 1997-12-27. New families of conservative systems on $S^2$ possessing an integral of fourth degree in momenta. https://arxiv.org/abs/dg-ga/9712018

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