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Nelin. Dinam., 2013, Volume 9, Number 1, Pages 51–58 (Mi nd369)  

This article is cited in 3 scientific papers (total in 3 papers)

On the motion of a mechanical system inside a rolling ball

Sergey V. Bolotina, Tatiana V. Popovab

a Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia
b M. V. Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider a mechanical system inside a rolling ball and show that if the ideal constraints have spherical symmetry, the equations of motion have a Lagrangian form. Without symmetry, this is not true.

Keywords: nonholonomic constraint, rolling ball, Lagrange equations, Hamilton principle.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 11.G34.31.0039
НШ-2519.2012.1
Russian Foundation for Basic Research 12-01-00441_а


Full text: PDF file (323 kB)
References: PDF file   HTML file
UDC: 531.36
MSC: 37J60, 37J35, 70E18
Received: 30.03.2012
Revised: 21.11.2012

Citation: Sergey V. Bolotin, Tatiana V. Popova, “On the motion of a mechanical system inside a rolling ball”, Nelin. Dinam., 9:1 (2013), 51–58

Citation in format AMSBIB
\Bibitem{BolPop13}
\by Sergey~V.~Bolotin, Tatiana~V.~Popova
\paper On the motion of a mechanical system inside a rolling ball
\jour Nelin. Dinam.
\yr 2013
\vol 9
\issue 1
\pages 51--58
\mathnet{http://mi.mathnet.ru/nd369}


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    This publication is cited in the following articles:
    1. T. B. Ivanova, E. N. Pivovarova, “Dinamika i upravlenie sfericheskim robotom s osesimmetrichnym mayatnikovym privodom”, Nelineinaya dinam., 9:3 (2013), 507–520  mathnet  crossref
    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. Yu. L. Karavaev, A. A. Kilin, “Dinamika sferorobota s vnutrennei omnikolesnoi platformoi”, Nelineinaya dinam., 11:1 (2015), 187–204  mathnet  elib
  • Нелинейная динамика
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