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Nelin. Dinam., 2012, Volume 8, Number 1, Pages 83–101 (Mi nd305)  

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

On the motion of free disc on the rough horisontal plane

T. V. Salnikovaab, D. V. Treschevab, S. R. Gallyamovc

a Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991, Russia
b Steklov Mathematical Institute, Gubkina st. 8, Moscow, 119991, Russia
c Udmurt State University, Universitetskaya st. 1, Izhevsk, 426034, Russia

Abstract: We consider the problem of a disk sliding on a horizontal plane under the action of dry friction forces. The model is based on three hypotheses. The law of interaction of a small element of the disk’s surface with the plane is the Amonton–Coulomb law, the pressure distribution over the contact patch is a linear (generally speaking, time-dependent) function of Cartesian coordinates, the height of the disk is not high. The equations of motion possess a rich group of symmetry, which enables a detailed qualitative analysis of the problem.

Keywords: dry friction, Amontons–Coulomb law

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 11.G34.31.0039

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Document Type: Article
UDC: 539.3
MSC: 70F40, 70F35, 70E18
Received: 07.04.2012

Citation: T. V. Salnikova, D. V. Treschev, S. R. Gallyamov, “On the motion of free disc on the rough horisontal plane”, Nelin. Dinam., 8:1 (2012), 83–101

Citation in format AMSBIB
\by T.~V.~Salnikova, D.~V.~Treschev, S.~R.~Gallyamov
\paper On the motion of free disc on the rough horisontal plane
\jour Nelin. Dinam.
\yr 2012
\vol 8
\issue 1
\pages 83--101

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    This publication is cited in the following articles:
    1. D. V. Treschev, N. N. Erdakova, T. B. Ivanova, “O finalnom dvizhenii tsilindricheskikh tel po sherokhovatoi ploskosti”, Nelineinaya dinam., 8:3 (2012), 585–603  mathnet
    2. D. S. Burlakov, A. A. Seslavina, “O dvizhenii tsilindricheskoi shaiby po gorizontalnoi ploskosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 4, 125–139  mathnet
    3. N. N. Erdakova, I. S. Mamaev, “Dinamika tela s osesimmetrichnym osnovaniem, skolzyaschego po sherokhovatoi ploskosti”, Nelineinaya dinam., 9:3 (2013), 521–545  mathnet
    4. Rozenblat G.M., “On a Disk Sliding on a Rough Inclined Plane Under an Arbitrary Law of Normal Stresses”, Mech. Sol., 48:5 (2013), 573–580  crossref  isi  elib  scopus
    5. Rusinova A.M., “The Dynamics of a Homogeneous Disc on an Inclined Plane with Friction”, J. Appl. Math. Mech., 77:4 (2013), 386–391  crossref  mathscinet  isi  elib  scopus
    6. G. M. Rozenblat, “A disk sliding along a rough inclined plane under an arbitrary normal-stress law”, Dokl. Phys., 59:3 (2014), 133–138  crossref  crossref  mathscinet  isi  elib  elib  scopus
    7. 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
    8. A. A. Zhulidova, “Force interaction simulation for the motion of a spherical segment on a spherical surface with friction”, Moscow University Mechanics Bulletin, 70:1 (2015), 13–18  mathnet  crossref
    9. G. P. Terekhov, V. E. Pavlovskii, “Upravlenie robotom-sharom s pomoschyu makhovikov”, Preprinty IPM im. M. V. Keldysha, 2017, 016, 31 pp.  mathnet  crossref
    10. E. I. Kugushev, T. V. Popova, “O dvizhenii shaiby po gorizontalnoi ploskosti v modeli vyazkogo treniya s peremennym koeffitsientom”, Nelineinaya dinam., 14:1 (2018), 145–153  mathnet  crossref  elib
  • Нелинейная динамика
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