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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
 References:
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Bibliographic databases:
  
Document Type:
Article
MSC: 70F40, 70E18
Received: 28.03.2013
Accepted:31.12.2013
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
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\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
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\crossref{https://doi.org/10.1134/S1560354714010080}
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Linking options:
http://mi.mathnet.ru/eng/rcd144 http://mi.mathnet.ru/eng/rcd/v19/i1/p116
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Zh. Zhao, C. Liu, B. Chen, B. Brogliato, “Asymptotic analysis of Painlevé's paradox”, Multibody Syst. Dyn., 35:3 (2015), 299–319
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A. R. Champneys, P. L. Varkonyi, “The Painlevé paradox in contact mechanics”, IMA J. Appl. Math., 81:3, SI (2016), 538–588
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B. Brogliato: Brogliato, B, Nonsmooth Mechanics: Models, Dynamics and Control, Communications and Control Engineering, 3Rd Edition, Springler, 2016
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T. B. Ivanova, I. S. Mamaev, “Dynamics of a Painlevé–Appell system”, J. Appl. Math. Mech., 80:1 (2016), 7–15
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