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On a family of integrable systems on $S^2$ with a cubic integral of motion

A. V. Tsiganov
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Abstract

We discuss a family of integrable systems on the sphere $S^2$ with an additional integral of third order in momenta. This family contains the Coryachev-Chaplygin top, the Goryachev system, the system recently discovered by Dullin and Matveev and two new integrable systems. On the non-physical sphere with zero radius all these systems are isomorphic to each other.

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A. V. Tsiganov. 2004-10-12. On a family of integrable systems on $S^2$ with a cubic integral of motion. https://doi.org/10.1088/0305-4470%2F38%2F4%2F011

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