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

Bernard Brogliato (1)

1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems

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.

Mots clés: quasi-velocities; quasi-Lagrange dynamics; kinematic impact law; Moreau's impact law; kinetic angles; kinetic metric.; kinetic metric; bilateral holonomic constraints; unilateral constraints; complementarity conditions; Coulomb friction; tangential restitution; Painlevé paradox

Domaines: Optimisation et contrôle [math.OC]

Bernard Brogliato. Kinetic quasi-velocities in unilaterally constrained Lagrangian mechanics with impacts and friction. [Research Report] RR-8158, INRIA. 2012. ⟨hal-00762986⟩