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LANS Publications

"Convergence of a Class of Semi-implicit Time-stepping Schemes for Nonsmooth Rigid Multibody Dynamics"

B. I. Gavrea, M. Anitescu, and F. A. Potra

SIAM J. on Optimization, vol. 19, no. 2, , pp. 969-1001. Also Preprint ANL/MCS-P1378-1006

Preprint Version: [pdf]

In this work we present a framework for the convergence analysis in a measure differential inclusion sense of a class of time-stepping schemes for multibody dynamics with contacts, joints, and friction. This class of methods solves one linear complementarity problem per step and contains the semi-implicit Euler method, as well as trapezoidal-like methods for which second-order convergence was recently proved under certain conditions. By using the concept of a reduced friction cone, the analysis includes, for the first time, a convergence result for the case that includes joints. An unexpected intermediary result is that we are able to define a discrete velocity function of bounded variation, although the natural discrete velocity function produced by our algorithm may have unbounded variation.