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Ball on a viscoelastic plane

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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.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    A. A. Zobova

  2. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    D. V. Treschev

Authors
  1. A. A. Zobova
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  2. D. V. Treschev
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Additional information

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2013, Vol. 281, pp. 98–126.

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Zobova, A.A., Treschev, D.V. Ball on a viscoelastic plane. Proc. Steklov Inst. Math. 281, 91–118 (2013). https://doi.org/10.1134/S0081543813040093

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  • DOI: https://doi.org/10.1134/S0081543813040093

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