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Regular and Chaotic Dynamics, 2016, Volume 21, Issue 2, Pages 204–231 (Mi rcd75)  
This article is cited in 6 scientific papers (total in 6 papers)

Dynamics of a Rolling and Sliding Disk in a Plane. Asymptotic Solutions, Stability and Numerical Simulations

Maria Przybylskaa, Stefan Rauch-Wojciechowskib

a Institute of Physics, University of Zielona Góra, Licealna 9, PL-65–417, Zielona Góra, Poland
b Department of Mathematics, Linköping University, 581 83, Linköping, Sweden
Citations (6)
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Abstract: We present a qualitative analysis of the dynamics of a rolling and sliding disk in a horizontal plane. It is based on using three classes of asymptotic solutions: straight-line rolling, spinning about a vertical diameter and tumbling solutions. Their linear stability analysis is given and it is complemented with computer simulations of solutions starting in the vicinity of the asymptotic solutions. The results on asymptotic solutions and their linear stability apply also to an annulus and to a hoop.
Keywords: rigid body, nonholonomic mechanics, rolling disk, sliding disk.
Funding agency Grant number
National Science Centre (Narodowe Centrum Nauki) DEC-2013/09/B/ST1/04130
M.P. has been supported by grant No. DEC-2013/09/B/ST1/04130 of the National Science Center of Poland, and M.P. and S.R. gracefully acknowledge support from the Department of Mathematics of Linköping University.
Received: 27.10.2015
Accepted: 15.02.2016
English version:

DOI: https://doi.org/10.1134/S1560354716020052
Bibliographic databases:
Document Type: Article
MSC: 37J60, 37J25, 70G45
Language: English
Citation: Maria Przybylska, Stefan Rauch-Wojciechowski, “Dynamics of a Rolling and Sliding Disk in a Plane. Asymptotic Solutions, Stability and Numerical Simulations”, Regul. Chaotic Dyn., 21:2 (2016), 204–231
Citation in format AMSBIB
\Bibitem{PrzRau16}
\by Maria Przybylska, Stefan Rauch-Wojciechowski
\paper Dynamics of a Rolling and Sliding Disk in a Plane. Asymptotic Solutions, Stability and Numerical Simulations
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 2
\pages 204--231
\mathnet{http://mi.mathnet.ru/rcd75}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3486006}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000374286800005}
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  • https://www.mathnet.ru/eng/rcd/v21/i2/p204
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:184
    References:36
     
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