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Tr. Mat. Inst. Steklova, 2013, Volume 281, Pages 98–126 (Mi tm3467)  

This article is cited in 4 scientific papers (total in 4 papers)

Ball on a viscoelastic plane

A. A. Zobovaa, D. V. Treschevb

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, Russia
b Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

Abstract: We consider dynamical problems arising in connection with the interaction of an absolutely rigid ball and a viscoelastic support plane. The support is a relatively stiff viscoelastic Kelvin–Voigt medium that coincides with the horizontal plane in the undeformed state. We also assume that under the deformation the support induces dry friction forces that are locally governed by the Coulomb law. We study the impact appearing when a ball falls on the plane. Another problem of our interest is the motion of a ball “along the plane”. A detailed analysis of various stages of the motion is presented. We also compare this model with classical models of interaction of solid bodies.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 11.G34.31.0039
Russian Foundation for Basic Research 12-01-31059
The work was supported by a grant of the Government of the Russian Federation (project no. 11.G34.31.0039) and in part by the Russian Foundation for Basic Research (project no. 12-01-31059).


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English version:
Proceedings of the Steklov Institute of Mathematics, 2013, 281, 91–118

Bibliographic databases:

UDC: 539.3
Received in July 2012

Citation: A. A. Zobova, D. V. Treschev, “Ball on a viscoelastic plane”, Modern problems of mechanics, Collected papers. Dedicated to Academician Andrei Gennad'evich Kulikovskii on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 281, MAIK Nauka/Interperiodica, Moscow, 2013, 98–126; Proc. Steklov Inst. Math., 281 (2013), 91–118

Citation in format AMSBIB
\by A.~A.~Zobova, D.~V.~Treschev
\paper Ball on a~viscoelastic plane
\inbook Modern problems of mechanics
\bookinfo Collected papers. Dedicated to Academician Andrei Gennad'evich Kulikovskii on the occasion of his 80th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2013
\vol 281
\pages 98--126
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\jour Proc. Steklov Inst. Math.
\yr 2013
\vol 281
\pages 91--118

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    This publication is cited in the following articles:
    1. 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
    2. A. A. Zobova, “A review of models of distributed dry friction”, Pmm-J. Appl. Math. Mech., 80:2 (2016), 141–148  crossref  mathscinet  isi  scopus
    3. A. V. Karapetyan, A. A. Zobova, “Tippe-top on visco-elastic plane: steady-state motions, generalized smale diagrams and overturns”, Lobachevskii J. Math., 38:6 (2017), 1007–1013  crossref  mathscinet  zmath  isi  scopus
    4. Zobova A.A., “Dry Friction Distributed Over a Contact Patch Between a Rigid Body and a Visco-Elastic Plane”, Multibody Syst. Dyn., 45:2 (2019), 203–222  crossref  mathscinet  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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