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Nonsmooth Lagrangian mechanics and variational collision integrators

Fetecau, R. C. and Marsden, J. E. and Ortiz, M. and West, M. (2003) Nonsmooth Lagrangian mechanics and variational collision integrators. SIAM Journal on Applied Dynamical Systems, 2 (3). pp. 381-416. ISSN 1536-0040. http://resolver.caltech.edu/CaltechAUTHORS:FETsiamjads03

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Abstract

Variational techniques are used to analyze the problem of rigid-body dynamics with impacts. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for collisions, and it is shown in what sense the system is symplectic and satisfies a Noether-style momentum conservation theorem. Discretizations of this nonsmooth mechanics are developed by using the methodology of variational discrete mechanics. This leads to variational integrators which are symplectic-momentum preserving and are consistent with the jump conditions given in the continuous theory. Specific examples of these methods are tested numerically, and the long-time stable energy behavior typical of variational methods is demonstrated.


Item Type:Article
Additional Information:© 2003 Society for Industrial and Applied Mathematics. Received by the editors April 23, 2002; accepted for publication (in revised form) by M. Golubitsky May 1, 2003; published electronically August 23, 2003.
Subject Keywords:discrete mechanics, variational integrators, collisions, RIGID-BODY DYNAMICS, HARD-CORE/CONTINUOUS POTENTIALS, FRICTIONAL CONTACT PROBLEMS, UNILATERAL CONSTRAINTS, SWEEPING PROCESS, DRY FRICTION, TIME, FORMULATION, IMPACT, ALGORITHM
Record Number:CaltechAUTHORS:FETsiamjads03
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:FETsiamjads03
Alternative URL:http://dx.doi.org/10.1137/S1111111102406038
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:800
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Oct 2005
Last Modified:26 Dec 2012 08:41

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