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Nelin. Dinam., 2012, Volume 8, Number 3, Pages 569–583 (Mi nd344)  

This article is cited in 4 scientific papers (total in 4 papers)

On the Routh sphere

Ivan A. Bizyaeva, Andrey V. Tsiganovb

a Institute of Computer Science, Udmurt State University Universitetskaya 1, Izhevsk, 426034, Russia
b Saint-Petersburg State University Universitetskaya nab. 7-9, St. Petersburg, 199034, Russia

Abstract: We discuss an embedding of the vector field associated with the nonholonomic Routh sphere in subgroup of the commuting Hamiltonian vector fields associated with this system. We prove that the corresponding Poisson brackets are reduced to canonical ones in the region without of homoclinic trajectories.

Keywords: nonholonomic mechanics, Routh sphere, Poisson brackets

Full text: PDF file (392 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 532.5
MSC: 37J60, 37J35, 53D17, 70E18, 70F25, 70H45
Received: 28.07.2012
Revised: 29.09.2012

Citation: Ivan A. Bizyaev, Andrey V. Tsiganov, “On the Routh sphere”, Nelin. Dinam., 8:3 (2012), 569–583

Citation in format AMSBIB
\Bibitem{BizTsi12}
\by Ivan~A.~Bizyaev, Andrey~V.~Tsiganov
\paper On the Routh sphere
\jour Nelin. Dinam.
\yr 2012
\vol 8
\issue 3
\pages 569--583
\mathnet{http://mi.mathnet.ru/nd344}


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    This publication is cited in the following articles:
    1. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Ierarkhiya dinamiki pri kachenii tverdogo tela bez proskalzyvaniya i vercheniya po ploskosti i sfere”, Nelineinaya dinam., 9:2 (2013), 141–202  mathnet
    2. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dinamika negolonomnykh sistem, sostoyaschikh iz sfericheskoi obolochki s podvizhnym tverdym telom vnutri”, Nelineinaya dinam., 9:3 (2013), 547–566  mathnet
    3. A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Geometrizatsiya teoremy Chaplygina o privodyaschem mnozhitele”, Nelineinaya dinam., 9:4 (2013), 627–640  mathnet
    4. A. V. Borisov, I. S. Mamaev, A. V. Tsiganov, “On the Nonlinear Poisson Bracket Arising in Nonholonomic Mechanics”, Math. Notes, 95:3 (2014), 308–315  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Нелинейная динамика
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