Nonsmooth Lagrangian Mechanics
and Variational Collision Integrators

Fetecau, R.C., J.E. Marsden, M. Ortiz, and M. West

SIAM J. Applied Dynamical Systems, 2, No. 3, 381-416

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.