On the generalized integrable Chaplygin system

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

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12 pages, standard LaTeX with AMS fonts

Scientific paper

10.1007/s10958-010-0036-5

We discuss two polynomial bi-Hamiltonian structures for the generalized
integrable Chaplygin system on the sphere S^2 with an additional integral of
fourth order in momenta. An explicit procedure to find the variables of
separation, the separation relations and the transformation of the
corresponding algebraic curves of genus two is considered in detail.

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