Nonsmooth analysis of three-dimensional slipping and rolling in the presence of dry friction

Mate Antali, Gabor Stepan

Research output: Contribution to journalArticle


In this paper, the nonsmooth dynamics of two contacting rigid bodies is analysed in the presence of dry friction. In three dimensions, slipping can occur in continuously many directions. Then, the Coulomb friction model leads to a system of differential equations, which has a codimension-2 discontinuity set in the phase space. The new theory of extended Filippov systems is applied to analyse the dynamics of a rigid body moving on a fixed rigid plane to explore the possible transitions between the slipping and rolling behaviour. The paper focuses on finding the so-called limit directions of the slipping equations at the discontinuity. This leads to a complete qualitative description of the possible scenarios of the dynamics in the vicinity of the discontinuity. It is shown that the new approach consistently extends the information provided from the static friction force of the rolling behaviour. The methods are demonstrated on an application example.

Original languageEnglish
Pages (from-to)1799-1817
Number of pages19
JournalNonlinear Dynamics
Issue number3
Publication statusPublished - Aug 1 2019


  • Coulomb friction
  • Filippov systems
  • Nonsmooth dynamics
  • Slipping

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

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