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.
Keywords:
nonholonomic mechanics, separation of variables, Chaplygin ball.
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
\Bibitem{Tsi19}
\by Andrey V. Tsiganov
\paper Hamiltonization and Separation of Variables for a Chaplygin Ball on a Rotating Plane
\jour Regul. Chaotic Dyn.
\yr 2019
\vol 24
\issue 2
\pages 171--186
\mathnet{http://mi.mathnet.ru/rcd451}
\crossref{https://doi.org/10.1134/S1560354719020035}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85064257548}
Linking options:
https://www.mathnet.ru/eng/rcd451
https://www.mathnet.ru/eng/rcd/v24/i2/p171
This publication is cited in the following 9 articles:
A. V. Tsyganov, “O tenzornykh invariantakh dlya integriruemykh sluchaev dvizheniya tverdogo tela Eilera, Lagranzha i Kovalevskoi”, Izv. RAN. Ser. matem., 89:2 (2025), 161–188
A. V. Tsiganov, E. O. Porubov, “On a class of quadratic conservation laws for Newton equations in Euclidean space”, Theoret. and Math. Phys., 216:2 (2023), 1209–1237
Evgeniya A. Mikishanina, “Dynamics of the Chaplygin sphere with additional constraint”, Commun. Nonlinear Sci. Numer. Simul., 117 (2023), 106920–15
Alexey V. Borisov, Andrey V. Tsiganov, “On the Nonholonomic Routh Sphere in a Magnetic Field”, Regul. Chaotic Dyn., 25:1 (2020), 18–32
A. V. Borisov, A. V. Tsiganov, “The motion of a nonholonomic Chaplygin sphere in a magnetic field, the Grioli problem, and the Barnett-London effect”, Dokl. Phys., 65:3 (2020), 90–93
Miguel D. Bustamante, Peter Lynch, “Nonholonomic Noetherian Symmetries and Integrals of the Routh Sphere and the Chaplygin Ball”, Regul. Chaotic Dyn., 24:5 (2019), 511–524
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Different Models of Rolling for a Robot Ball on a Plane as a Generalization of the Chaplygin Ball Problem”, Regul. Chaotic Dyn., 24:5 (2019), 560–582
Alexey V. Borisov, Andrey V. Tsiganov, “On the Chaplygin Sphere in a Magnetic Field”, Regul. Chaotic Dyn., 24:6 (2019), 739–754
A. V. Borisov, A. V. Tsyganov, “Vliyanie effektov Barnetta-Londona i Einshteina-de Gaaza na dvizhenie negolonomnoi sfery Rausa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:4 (2019), 583–598
Citation in format AMSBIB
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