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Hamiltonization and Separation of Variables for a Chaplygin Ball on a Rotating Plane

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Abstract

We discuss a non-Hamiltonian vector field appearing in considering the partial motion of a Chaplygin ball rolling on a horizontal plane which rotates with constant angular velocity. In two partial cases this vector field is expressed via Hamiltonian vector fields using a nonalgebraic deformation of the canonical Poisson bivector on e*(3). For the symmetric ball we also calculate variables of separation, compatible Poisson brackets, the algebra of Haantjes operators and 2 × 2 Lax matrices.

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Authors and Affiliations

  1. St. Petersburg State University, ul. Ulyanovskaya 1, St. Petersburg, 198504, Russia

    Andrey V. Tsiganov

  2. Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia

    Andrey V. Tsiganov

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  1. Andrey V. Tsiganov
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Tsiganov, A.V. Hamiltonization and Separation of Variables for a Chaplygin Ball on a Rotating Plane. Regul. Chaot. Dyn. 24, 171–186 (2019). https://doi.org/10.1134/S1560354719020035

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  • DOI: https://doi.org/10.1134/S1560354719020035

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