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Regul. Chaotic Dyn., 2014, Volume 19, Issue 1, Pages 116–139 (Mi rcd144)  

This article is cited in 9 scientific papers (total in 10 papers)

The Dynamics of a Rigid Body with a Sharp Edge in Contact with an Inclined Surface in the Presence of Dry Friction

Ivan S. Mamaeva, Tatiana B. Ivanovab

a Institute of Computer Science, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
b Faculty of Physics and Energetics, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia

Abstract: In this paper we consider the dynamics of a rigid body with a sharp edge in contact with a rough plane. The body can move so that its contact point is fixed or slips or loses contact with the support. In this paper, the dynamics of the system is considered within three mechanical models which describe different regimes of motion. The boundaries of the domain of definition of each model are given, the possibility of transitions from one regime to another and their consistency with different coefficients of friction on the horizontal and inclined surfaces are discussed.

Keywords: rod, Painlevé paradox, dry friction, loss of contact, frictional impact

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation NSh-2964.2014.1
MK-2171.2014.1
1.1248.2011
This research was supported by the analytical departmental target program “Development of Scientific Potential of Higher Schools” for 2012–2014, No 1.1248.2011 “Nonholonomic Dynamical Systems and Control Problems” and by the Grant of the President of the Russian Federation for Support of Leading Scientific Schools NSh-2964.2014.1. The work of T. B.Ivanova was supported by the Grant of the President of the Russian Federation for Support of Young Candidates of Science MK-2171.2014.1.


DOI: https://doi.org/10.1134/S1560354714010080

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Document Type: Article
MSC: 70F40, 70E18
Received: 28.03.2013
Language: English

Citation: Ivan S. Mamaev, Tatiana B. Ivanova, “The Dynamics of a Rigid Body with a Sharp Edge in Contact with an Inclined Surface in the Presence of Dry Friction”, Regul. Chaotic Dyn., 19:1 (2014), 116–139

Citation in format AMSBIB
\Bibitem{MamIva14}
\by Ivan~S.~Mamaev, Tatiana~B.~Ivanova
\paper The Dynamics of a Rigid Body with a Sharp Edge in Contact with an Inclined Surface in the Presence of Dry Friction
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 1
\pages 116--139
\mathnet{http://mi.mathnet.ru/rcd144}
\crossref{https://doi.org/10.1134/S1560354714010080}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3181040}
\zmath{https://zbmath.org/?q=an:06506694}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000333239100008}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Alexander P. Ivanov, “On the Impulsive Dynamics of M-blocks”, Regul. Chaotic Dyn., 19:2 (2014), 214–225  mathnet  crossref  mathscinet  zmath
    2. Yizhar Or, “Painlevé’s Paradox and Dynamic Jamming in Simple Models of Passive Dynamic Walking”, Regul. Chaotic Dyn., 19:1 (2014), 64–80  mathnet  crossref  mathscinet  zmath
    3. Yu. L. Karavaev, A. A. Kilin, “Dinamika sferorobota s vnutrennei omnikolesnoi platformoi”, Nelineinaya dinam., 11:1 (2015), 187–204  mathnet  elib
    4. A. V. Borisov, I. S. Mamaev, “Notes on new friction models and nonholonomic mechanics”, Phys. Usp., 58:12 (2015), 1220–1222  mathnet  crossref  crossref  adsnasa  isi  elib
    5. Zh. Zhao, C. Liu, B. Chen, B. Brogliato, “Asymptotic analysis of Painlevé's paradox”, Multibody Syst. Dyn., 35:3 (2015), 299–319  crossref  mathscinet  zmath  isi  scopus
    6. Yury L. Karavaev, Alexander A. Kilin, “The Dynamics and Control of a Spherical Robot with an Internal Omniwheel Platform”, Regul. Chaotic Dyn., 20:2 (2015), 134–152  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    7. T. B. Ivanova, N. N. Erdakova, Yu. L. Karavaev, “Experimental investigation of the dynamics of a brake shoe”, Dokl. Phys., 61:12 (2016), 611–614  crossref  isi  scopus
    8. A. R. Champneys, P. L. Varkonyi, “The Painlevé paradox in contact mechanics”, IMA J. Appl. Math., 81:3, SI (2016), 538–588  crossref  mathscinet  isi  scopus
    9. B. Brogliato: Brogliato, B, Nonsmooth Mechanics: Models, Dynamics and Control, Communications and Control Engineering, 3Rd Edition, Springler, 2016  crossref  mathscinet  isi  scopus
    10. T. B. Ivanova, I. S. Mamaev, “Dynamics of a Painlevé–Appell system”, J. Appl. Math. Mech., 80:1 (2016), 7–15  crossref  mathscinet  isi  scopus
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