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

Laetitia Paoli

doi:10.3934/dcdss.2013.6.1609

Article Contents

2013, Volume 6, Issue 6: 1609-1619. Doi: 10.3934/dcdss.2013.6.1609

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

Laetitia Paoli^1,

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

Received: May 31, 2012

Revised: August 31, 2012

Published: November 2013

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Abstract

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.

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

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References

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