Article Contents
Article Contents

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

• 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.
Mathematics Subject Classification: Primary: 34A60, 34A12, 70E55; Secondary: 65N20.

 Citation:

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