# American Institute of Mathematical Sciences

December  2013, 6(6): 1609-1619. doi: 10.3934/dcdss.2013.6.1609

## A velocity-based time-stepping scheme for multibody dynamics with unilateral constraints

 1 PRES Université de Lyon, UJM F-42023, CNRS UMR 5208, Institut Camille Jordan, 23 rue du Docteur Paul Michelon, 42023 Saint-Etienne Cedex 2, France

Received  June 2012 Revised  September 2012 Published  April 2013

We consider a system of rigid bodies subjected to some non penetration conditions characterized by the inequalities $f_{\alpha} (q) \ge 0$, $\alpha \in \{1, \dots, \nu\}$, $\nu \ge 1$, for the configuration $q \in \mathbb{R}^d$. We assume that there is no adhesion and no friction during contact and we model the behaviour of the system at impact by a Newton's law. Starting from the mechanical description of the problem, we derive two mathematical formulations, using either the configuration or the generalized velocity as unknown. Then a velocity-based time-stepping scheme, inspired by the catching-up algorithms, is presented and its convergence in the multi-constraint case (i.e $\nu \ge1$) is stated.
Citation: Laetitia Paoli. A velocity-based time-stepping scheme for multibody dynamics with unilateral constraints. Discrete & Continuous Dynamical Systems - S, 2013, 6 (6) : 1609-1619. doi: 10.3934/dcdss.2013.6.1609
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