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Nelin. Dinam., 2012, Volume 8, Number 1, Pages 103–111 (Mi nd306)  

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

The dynamics of the Chaplygin ball with a fluid-filled cavity

A. V. Borisov, I. S. Mamaev

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

Abstract: We consider the problem of rolling of a ball with an ellipsoidal cavity filled with an ideal fluid, which executes a uniform vortex motion, on an absolutely rough plane. We point out the case of existence of an invariant measure and show that there is a particular case of integrability under conditions of axial symmetry

Keywords: vortex motion, non-holonomic constraint, Chaplygin ball, invariant measure, integrability, rigid body, ideal fluid

Full text: PDF file (270 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 531.7
MSC: 70E18, 76B47
Received: 25.11.2011

Citation: A. V. Borisov, I. S. Mamaev, “The dynamics of the Chaplygin ball with a fluid-filled cavity”, Nelin. Dinam., 8:1 (2012), 103–111

Citation in format AMSBIB
\Bibitem{BorMam12}
\by A.~V.~Borisov, I.~S.~Mamaev
\paper The dynamics of the Chaplygin ball with a fluid-filled cavity
\jour Nelin. Dinam.
\yr 2012
\vol 8
\issue 1
\pages 103--111
\mathnet{http://mi.mathnet.ru/nd306}


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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. Borisov, I. S. Mamaev, I. A. Bizyaev, “The Jacobi Integral in Nonholonomic Mechanics”, Regul. Chaotic Dyn., 20:3 (2015), 383–400  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    4. Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “Dynamics and Control of an Omniwheel Vehicle”, Regul. Chaotic Dyn., 20:2 (2015), 153–172  mathnet  crossref  mathscinet  zmath  adsnasa
  • Нелинейная динамика
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