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Regul. Chaotic Dyn., 2014, Volume 19, Issue 6, Pages 607–634 (Mi rcd187)  

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

The Dynamics of a Body with an Axisymmetric Base Sliding on a Rough Plane

Alexey V. Borisovab, Nadezhda N. Erdakovab, Tatiana B. Ivanovaab, Ivan S. Mamaevc

a Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, 141700 Russia
b Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
c Kalashnikov Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, 426069 Russia

Abstract: In this paper we investigate the dynamics of a body with a flat base sliding on a horizontal and inclined rough plane under the assumption of linear pressure distribution of the body on the plane as the simplest dynamically consistent friction model. For analysis we use the descriptive function method similar to the methods used in the problems of Hamiltonian dynamics with one degree of freedom and allowing a qualitative analysis of the system to be made without explicit integration of equations of motion. In addition, we give a systematic review of the well-known experimental and theoretical results in this area.

Keywords: dry friction, linear pressure distribution, planar motion, Coulomb law

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation
MK-2171.2014.1
Russian Foundation for Basic Research 14-01-00289-a
This work was supported by the Ministry of Education and Science of the Russian Federation within the framework of the basic part of the state assignment to institutions of higher education. 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 and by the RFBR Grant 14-01-00289-a.


DOI: https://doi.org/10.1134/S1560354714060021

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Document Type: Article
MSC: 70F40, 70F35, 70E18
Received: 02.09.2014
Accepted:16.10.2014
Language: English

Citation: Alexey V. Borisov, Nadezhda N. Erdakova, Tatiana B. Ivanova, Ivan S. Mamaev, “The Dynamics of a Body with an Axisymmetric Base Sliding on a Rough Plane”, Regul. Chaotic Dyn., 19:6 (2014), 607–634

Citation in format AMSBIB
\Bibitem{BorErdIva14}
\by Alexey~V.~Borisov, Nadezhda~N.~Erdakova, Tatiana~B.~Ivanova, Ivan~S.~Mamaev
\paper The Dynamics of a Body with an Axisymmetric Base Sliding on a Rough Plane
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 6
\pages 607--634
\mathnet{http://mi.mathnet.ru/rcd187}
\crossref{https://doi.org/10.1134/S1560354714060021}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3284604}
\zmath{https://zbmath.org/?q=an:06507822}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000345996200002}


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    2. Nikolay A. Kudryashov, Dmitry I. Sinelshchikov, “On the Connection of the Quadratic Lienard Equation with an Equation for the Elliptic Functions”, Regul. Chaotic Dyn., 20:4 (2015), 486–496  mathnet  crossref  mathscinet  zmath  adsnasa  elib
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    4. Alexey V. Borisov, Yury L. Karavaev, Ivan S. Mamaev, Nadezhda N. Erdakova, Tatyana B. Ivanova, Valery V. Tarasov, “Experimental Investigation of the Motion of a Body with an Axisymmetric Base Sliding on a Rough Plane”, Regul. Chaotic Dyn., 20:5 (2015), 518–541  mathnet  crossref  mathscinet  zmath
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    6. N. A. Kudryashov, D. I. Sinelshchikov, “On the Integrability Conditions for a Family of Liénard-type Equations”, Regul. Chaotic Dyn., 21:5 (2016), 548–555  mathnet  crossref
    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. P. Ivanov, N. N. Erdakova, “On a mechanical lens”, Int. J. Non-Linear Mech., 79 (2016), 115–121  crossref  isi  scopus
    9. A. V. Borisov, I. S. Mamaev, N. N. Erdakova, “Dynamics of a body sliding on a rough plane and supported at three points”, Theor. Appl. Mech., 43:2 (2016), 169–190  crossref  isi  scopus
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