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Nelin. Dinam., 2011, Volume 7, Number 3, Pages 559–568 (Mi nd277)  

This article is cited in 5 scientific papers (total in 5 papers)

Two non-holonomic integrable systems of coupled rigid bodies

A. V. Borisovab, I. S. Mamaevba

a Udmurt State University, Universitetskaya 1, Izhevsk, 426034 Russia
b Institute of Computer Science, Universitetskaya 1, Izhevsk, 426034 Russia

Abstract: The paper considers two new integrable systems due to Chaplygin, which describe the rolling of a spherical shell on a plane, with a ball or Lagranges gyroscope inside. All necessary first integrals and an invariant measure are found. The reduction to quadratures is given.

Keywords: non-holonomic constraint; integrability; invariant measure; gyroscope; quadrature; coupled rigid bodies

Full text: PDF file (415 kB)
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Document Type: Article
UDC: 532.5
MSC: 37J60
Received: 26.08.2011
Revised: 14.09.2011

Citation: A. V. Borisov, I. S. Mamaev, “Two non-holonomic integrable systems of coupled rigid bodies”, Nelin. Dinam., 7:3 (2011), 559–568

Citation in format AMSBIB
\Bibitem{BorMam11}
\by A.~V.~Borisov, I.~S.~Mamaev
\paper Two non-holonomic integrable systems of coupled rigid bodies
\jour Nelin. Dinam.
\yr 2011
\vol 7
\issue 3
\pages 559--568
\mathnet{http://mi.mathnet.ru/nd277}


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    This publication is cited in the following articles:
    1. E. N. Pivovarova, T. B. Ivanova, “Issledovanie ustoichivosti periodicheskikh reshenii v zadache o kachenii shara s mayatnikom”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 4, 146–155  mathnet
    2. 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
    3. T. B. Ivanova, E. N. Pivovarova, “Dinamika i upravlenie sfericheskim robotom s osesimmetrichnym mayatnikovym privodom”, Nelineinaya dinam., 9:3 (2013), 507–520  mathnet  crossref
    4. 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
    5. Balandin D.V., Komarov M.A., Osipov G.V., “A Motion Control for a Spherical Robot with Pendulum Drive”, J. Comput. Syst. Sci. Int., 52:4 (2013), 650–663  crossref  mathscinet  zmath  isi  elib  scopus
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