Variational collision integrators

RAZVAN FETECAU
Department of Applied and Computational Mathematics, 217-50
California Institute of Technology
Pasadena, CA 91125-5000, USA
van@acm.caltech.edu

Abstract:

We use variational techniques 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.