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 Regul. Chaotic Dyn., 2018, Volume 23, Issue 7-8, Pages 887–907 (Mi rcd373)

Integrable Nonsmooth Nonholonomic Dynamics of a Rubber Wheel with Sharp Edges

Alexander A. Kilin, Elena N. Pivovarova

Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: This paper is concerned with the dynamics of a wheel with sharp edges moving on a horizontal plane without slipping and rotation about the vertical (nonholonomic rubber model). The wheel is a body of revolution and has the form of a ball symmetrically truncated on both sides. This problem is described by a system of differential equations with a discontinuous right-hand side. It is shown that this system is integrable and reduces to quadratures. Partial solutions are found which correspond to fixed points of the reduced system. A bifurcation analysis and a classification of possible types of the wheel’s motion depending on the system parameters are presented.

Keywords: integrable system, system with a discontinuous right-hand side, nonholonomic constraint, bifurcation diagram, body of revolution, sharp edge, wheel, rubber model

 Funding Agency Grant Number Russian Science Foundation 14-50-00005 This research was carried out at the Steklov Mathematical Institute of the Russian Academy of Sciences and was supported by the Russian Science Foundation (project 14-50-00005).

DOI: https://doi.org/10.1134/S1560354718070067

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MSC: 70E15, 70E18, 70E40, 37Jxx
Accepted:03.12.2018
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Citation: Alexander A. Kilin, Elena N. Pivovarova, “Integrable Nonsmooth Nonholonomic Dynamics of a Rubber Wheel with Sharp Edges”, Regul. Chaotic Dyn., 23:7-8 (2018), 887–907

Citation in format AMSBIB
\Bibitem{KilPiv18} \by Alexander A. Kilin, Elena N. Pivovarova \paper Integrable Nonsmooth Nonholonomic Dynamics of a Rubber Wheel with Sharp Edges \jour Regul. Chaotic Dyn. \yr 2018 \vol 23 \issue 7-8 \pages 887--907 \mathnet{http://mi.mathnet.ru/rcd373} \crossref{https://doi.org/10.1134/S1560354718070067} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3910172} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000458183900006} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85061246519} 

• http://mi.mathnet.ru/eng/rcd373
• http://mi.mathnet.ru/eng/rcd/v23/i7/p887

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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. Alexander A. Kilin, Elena N. Pivovarova, “Qualitative Analysis of the Nonholonomic Rolling of a Rubber Wheel with Sharp Edges”, Regul. Chaotic Dyn., 24:2 (2019), 212–233
2. A. V. Borisov, A. V. Tsyganov, “Vliyanie effektov Barnetta-Londona i Einshteina-de Gaaza na dvizhenie negolonomnoi sfery Rausa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:4 (2019), 583–598
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