Time-Stepping Approximation of Rigid-Body Dynamics with Perfect Unilateral Constraints. II: The Partially Elastic Impact Case
Résumé
As in Paoli (Arch Rational Mech Anal, 2010), we consider a discrete mechanical system with a non-trivial mass matrix subjected to perfect unilateral constraints described by geometrical inequalities $f_\alpha (q)\geq 0$, $\alpha\in\{1,\ldots, ν\}$ $(ν\geq 1)$, but we assume now that the transmission of the velocities at impacts is governed by Newton's Law with a coefficient of restitution $e \in (0, 1]$ (so that the impact is partially elastic). We generalize the time-discretization of the second order differential inclusion describing the dynamics proposed in Paoli (Arch Rational Mech Anal, 2010) to this case and, once again, we prove its convergence.
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