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This article is cited in 8 scientific papers (total in 8 papers)
Hamiltonization and Separation of Variables for a Chaplygin Ball on a Rotating Plane
Andrey V. Tsiganovab a St. Petersburg State University, ul. Ulyanovskaya 1, St. Petersburg, 198504 Russia
b Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
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 $2\times2$ Lax matrices.
Keywords:
nonholonomic mechanics, separation of variables, Chaplygin ball.
Received: 14.01.2019 Accepted: 04.03.2019
Citation:
Andrey V. Tsiganov, “Hamiltonization and Separation of Variables for a Chaplygin Ball on a Rotating Plane”, Regul. Chaotic Dyn., 24:2 (2019), 171–186
Linking options:
https://www.mathnet.ru/eng/rcd451 https://www.mathnet.ru/eng/rcd/v24/i2/p171
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Abstract page: | 157 | References: | 24 |
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