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The contact problem in Lagrangian systems with redundant frictional bilateral and unilateral constraints and singular mass matrix. The all-sticking contacts problem

  • Bernard BrogliatoEmail author
  • Jozsef Kovecses
  • Vincent Acary
Article
  • 38 Downloads

Abstract

In this article we analyze the following problem: given a mechanical system subject to (possibly redundant) bilateral and unilateral constraints with set-valued Coulomb’s friction, provide conditions such that the state, which consists of all contacts sticking in both tangential and normal directions, is solvable. The analysis uses complementarity problems, variational inequalities, and linear algebra, hence it provides criteria which are, in principle, numerically tractable. An algorithm and several illustrating examples are proposed.

Keywords

Lagrangian systems Set-valued friction Complementarity conditions Contact problem Redundant constraints Singular mass matrix Variational inequality Tangent cone Normal cone Force closure Form closure 

Notes

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Authors and Affiliations

  1. 1.Inria, CNRS, Grenoble INP, LJKUniv. Grenoble AlpesGrenobleFrance
  2. 2.Mechanical Engineering Department, Macdonald Engineering BuildingMcGill UniversityMontrealCanada

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