We consider two polynomial bi—Harnilt0nian structures for the generalized integrable Chaplygin system on the sphere S 2 with an additional integral of fourth order in momenta. An explicit procedure for finding variables of separation, separation relations, and transformation of the corresponding algebraic curves of genus two is considered in detail. Bibliography: 21 titles.
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Published in Zapiski Nauchnykh Seminamv POMI, Vol. 374, 2010, pp. 250–267.
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Tsiganov, A.V. On the generalized Chaplygin system. J Math Sci 168, 901–911 (2010). https://doi.org/10.1007/s10958-010-0036-5
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DOI: https://doi.org/10.1007/s10958-010-0036-5