On a family of integrable systems on S2 with a cubic integral of motion
Abstract
We discuss a family of integrable systems on the sphere S2 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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