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

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. O...

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Bibliographic Details
Published inMultibody system dynamics Vol. 38; no. 1; pp. 43 - 76
Main Authors Blumentals, Alejandro, Brogliato, Bernard, Bertails-Descoubes, Florence
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.09.2016
Springer Verlag
Subjects
Automotive Engineering
Control
Dynamical Systems
Electrical Engineering
Engineering
Engineering Sciences
Mathematics
Mechanical Engineering
Mechanics
Optimization
Optimization and Control
Physics
Solid mechanics
Vibration
Lagrangian systems
Gauss’ principle
KKT conditions
Unilateral constraint
Bilateral constraint
Complementarity problem
Coulomb’s friction
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Summary: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.
ISSN:1384-5640
1573-272X
DOI:10.1007/s11044-016-9527-6