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Published 2003 | Published
Journal Article Open

Nonsmooth Lagrangian mechanics and variational collision integrators

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.

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. The research of this author was partially supported by the California Institute of Technology and the National Science Foundation.

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August 21, 2023
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