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Regular and Chaotic Dynamics, 2013, Volume 18, Issue 1-2, Pages 144–158
DOI: https://doi.org/10.1134/S1560354713010103 (Mi rcd101) 		 
This article is cited in 74 scientific papers (total in 74 papers)

How to Control the Chaplygin Ball Using Rotors. II

Alexey V. Borisovabc, Alexander A. Kilinbac, Ivan S. Mamaevcba

a Institute of Computer Science; Laboratory of Nonlinear Analysis and the Design of New Types of Vehicles, Udmurt State University, Universitetskaya 1, Izhevsk, 426034 Russia
b Institute of Mathematics and Mechanics of the Ural Branch of RAS, S. Kovalevskaja str. 16, Ekaterinburg, 620990, Russia
c A.A. Blagonravov Mechanical Engineering Research Institute of RAS, Bardina str. 4, Moscow, 117334, Russia
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DOI: https://doi.org/10.1134/S1560354713010103
Abstract: In our earlier paper [3] we examined the problem of control of a balanced dynamically nonsymmetric sphere with rotors with no-slip condition at the point of contact. In this paper we investigate the controllability of a ball in the presence of friction. We also study the problem of the existence and stability of singular dissipation-free periodic solutions for a free ball in the presence of friction forces. The issues of constructive realization of the proposed algorithms are discussed.
Keywords: non-holonomic constraint, control, dry friction, viscous friction, stability, periodic solutions.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation NSh-2519.2012.1
1.1248.2011
1.7734.2013
1.7734.2013
This research was supported by the Presidential grant of leading scientific schools NSh-2519.2012.1. and Target Programmes for 2012–2014 (State contract 1.1248.2011, 1.7734.2013, 1.7734.2013).
Received: 12.12.2012
Accepted: 16.02.2013
Bibliographic databases:
Document Type: Article
MSC: 37J60, 37J35, 70E18, 70F25, 70H45
Language: English
Citation: Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “How to Control the Chaplygin Ball Using Rotors. II”, Regul. Chaotic Dyn., 18:1-2 (2013), 144–158
Citation in format AMSBIB
\Bibitem{BorKilMam13}
\by Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev
\paper How to Control the Chaplygin Ball Using Rotors. II
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 1-2
\pages 144--158
\mathnet{http://mi.mathnet.ru/rcd101}
\crossref{https://doi.org/10.1134/S1560354713010103}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3040988}
\zmath{https://zbmath.org/?q=an:1303.37021}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000317623400010}
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  • https://www.mathnet.ru/eng/rcd101
  • https://www.mathnet.ru/eng/rcd/v18/i1/p144
    Comments
    This publication is cited in the following 74 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:86
     
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