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

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

2004-10-12

arxiv.org/abs/nlin/0410014v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTeX, 8 pages

Scientific paper

10.1088/0305-4470/38/4/011

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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