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Regul. Chaotic Dyn., 2016, Volume 21, Issue 7-8, Pages 804–810 (Mi rcd226)  

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

On Final Motions of a Chaplygin Ball on a Rough Plane

Alexander P. Ivanov

Moscow Institute of Physics and Technology, Inststitutskii per. 9, Dolgoprudnyi, 141700 Russia

Abstract: A heavy balanced nonhomogeneous ball moving on a rough horizontal plane is considered. The classical model of a “marble” body means a single point of contact, where sliding is impossible. We suggest that the contact forces be described by Coulomb’s law and show that in the final motion there is no sliding. Another, relatively new, contact model is the “rubber” ball: there is no sliding and no spinning. We treat this situation by applying a local Coulomb law within a small contact area. It is proved that the final motion of a ball with such friction is the motion of the “rubber” ball.

Keywords: Coulomb friction, Chaplygin ball, asymptotic dynamics

DOI: https://doi.org/10.1134/S1560354716070030

References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 70E18, 70F25
Received: 13.11.2016
Language: English

Citation: Alexander P. Ivanov, “On Final Motions of a Chaplygin Ball on a Rough Plane”, Regul. Chaotic Dyn., 21:7-8 (2016), 804–810

Citation in format AMSBIB
\Bibitem{Iva16}
\by Alexander P. Ivanov
\paper On Final Motions of a Chaplygin Ball on a Rough Plane
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 7-8
\pages 804--810
\mathnet{http://mi.mathnet.ru/rcd226}
\crossref{https://doi.org/10.1134/S1560354716070030}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000403091800003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85016028953}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Alexey V. Borisov, Alexey O. Kazakov, Elena N. Pivovarova, “Regular and Chaotic Dynamics in the Rubber Model of a Chaplygin Top”, Regul. Chaotic Dyn., 21:7-8 (2016), 885–901  mathnet  crossref
    2. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. A. P. Ivanov, “On singular points of equations of mechanics”, Dokl. Math., 97:2 (2018), 167–169  crossref  zmath  isi  scopus
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