Convergence of a class of semi-implicit time-stepping schemes for nonsmooth rigid multibody dynamics.
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.
- Research Organization:
- Argonne National Laboratory (ANL)
- Sponsoring Organization:
- NSF; SC
- DOE Contract Number:
- AC02-06CH11357
- OSTI ID:
- 957386
- Report Number(s):
- ANL/MCS/JA-59085
- Journal Information:
- SIAM J. Optimization, Journal Name: SIAM J. Optimization Journal Issue: 2 ; 2008 Vol. 19; ISSN 1052-6234
- Country of Publication:
- United States
- Language:
- ENGLISH
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