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 Regul. Chaotic Dyn.: Year: Volume: Issue: Page: Find

 Regul. Chaotic Dyn., 2019, Volume 24, Issue 2, Pages 171–186 (Mi rcd451)

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

 Funding Agency Grant Number Russian Science Foundation 15-12-20035 The work was supported by the Russian Science Foundation (project 15-12-20035).

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

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Bibliographic databases:

MSC: 37J60, 37J35, 70E18, 53D17
Accepted:04.03.2019
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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

Citation in format AMSBIB
\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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000464704800003} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85064257548}