The contact problem in Lagrangian systems subject to bilateral and unilateral constraints, with or without sliding Coulomb's friction: A tutorial - Archive ouverte HAL Access content directly
Journal Articles Multibody System Dynamics Year : 2016

The contact problem in Lagrangian systems subject to bilateral and unilateral constraints, with or without sliding Coulomb's friction: A tutorial

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Abstract

This work deals with the existence and uniqueness of the acceleration and contact forces for Lagrangian systems subject to bilateral and/or unilateral constraints with or without sliding Coulomb’s friction. Sliding friction is known to yield singularities in the system, such as Painlevé’s paradox. Our work aims at providing sufficient conditions on the parameters of the system so that singularities are avoided (i.e., the contact problem is at least solvable). To this end, the frictional problem is treated as a perturbation of the frictionless case. We provide explicit criteria, in the form of calculable upper bounds on the friction coefficients, under which the frictional contact problem is guaranteed to remain well-posed. Complementarity problems, variational inequalities, quadratic programs and inclusions in normal cones are central tools.
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Dates and versions

hal-01096394 , version 1 (17-12-2014)
hal-01096394 , version 2 (01-11-2017)

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Alejandro Blumentals, Bernard Brogliato, Florence Bertails-Descoubes. The contact problem in Lagrangian systems subject to bilateral and unilateral constraints, with or without sliding Coulomb's friction: A tutorial. Multibody System Dynamics, 2016, 38 (1), pp.43-76. ⟨10.1007/s11044-016-9527-6⟩. ⟨hal-01096394v2⟩
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