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Regular and Chaotic Dynamics

, Volume 19, Issue 3, pp 296–309 | Cite as

A rigid body on a surface with random roughness

  • Daniil Burlakov
  • Dmitry Treschev
Article

Abstract

Consider an interval on a horizontal line with random roughness. With probability one it is supported at two points: one on the left, and another on the right from its center. We compute the probability distribution of the support points provided the roughness is fine grained. We also solve an analogous problem where a circle or a disk lies on a rough plane. Some applications in static are given.

Keywords

rigid body support with random roughness 

MSC2010 numbers

47N30 70C20 

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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityVorob’evy gory, MoscowRussia
  2. 2.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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