Time-Stepping Approximation of Rigid-Body Dynamics with Perfect Unilateral Constraints. I: The Inelastic Impact Case

Laetitia Paoli (1)

1 LA MUSE - Laboratoire de Mathématiques Unifiées de Saint-Etienne

We consider a discrete mechanical system with a non-trivial mass matrix, subjected to perfect unilateral constraints described by the geometrical inequalities $f _\alpha(q)\geq 0$, $\alpha\in\{1,\ldots, ν\}$ ($ν \geq 1$). We assume that the transmission of the velocities at impact is governed by Newton's Law with a coefficient of restitution $e = 0$ (so that the impact is inelastic). We propose a time-discretization of the second order differential inclusion describing the dynamics, which generalizes the scheme proposed in Paoli (J Differ Equ 211:247–281, 2005) and, for any admissible data, we prove the convergence of approximate motions to a solution of the initial-value problem.

Domaines: Systèmes dynamiques [math.DS]

Laetitia Paoli. Time-Stepping Approximation of Rigid-Body Dynamics with Perfect Unilateral Constraints. I: The Inelastic Impact Case. Archive for Rational Mechanics and Analysis, 2010, 198 (2), pp.457-503. ⟨10.1007/s00205-010-0311-0⟩. ⟨hal-01566929⟩