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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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.
|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|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||05 Oct 2005|
|Last Modified:||26 Dec 2012 08:41|
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