On the case of Goryachev-Chaplygin and new examples of integrable conservative systems on S^2

Details On the case of Goryachev-Chaplygin and new examples of integrable conservative systems on S^2 On the case of Goryachev-Chaplygin and new examples of integrable conservative systems on S^2

1998-01-28

arxiv.org/abs/math/9801124v1

Mathematics

Differential Geometry

16 pages, LaTex

Scientific paper

The aim of this paper is to describe a class of conservative systems on $S^2$ possessing an integral cubic in momenta. We prove that this class of systems consists off the case of Goryachev-Chaplygin, the one-parameter family of systems which has been found by the author in the previous paper (dg-ga/9711005) and a new two-parameter family of conservative systems on $S^2$ possessing an integral cubic in momenta.

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