Multibody System Dynamics

, Volume 32, Issue 2, pp 175–216 | Cite as

Kinetic quasi-velocities in unilaterally constrained Lagrangian mechanics with impacts and friction

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Abstract

Quasi-velocities computed with the kinetic metric of a Lagrangian system are introduced, and the quasi-Lagrange equations are derived with and without friction. This is shown to be very well suited to systems subject to unilateral constraints (hence varying topology) and impacts. Energetical consistency of a generalized kinematic impact law is carefully studied, both in the frictionless and the frictional cases. Some results concerning the existence and uniqueness of solutions to the so-called contact linear complementarity problem, when friction is present, are provided.

Keywords

Bilateral holonomic constraints Unilateral constraints Complementarity conditions Coulomb friction Tangential restitution Painlevé paradox Quasi-velocities Quasi-Lagrange dynamics Kinematic impact law Moreau’s impact law Kinetic angles Kinetic metric 
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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Bipop team-project, ZIRST MontbonnotINRIASaint-Ismier cedexFrance

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