Stabilization of constrained mechanical systems with DAEs and invariant manifolds (1994)
| Venue: | J. Mech. Struct. Machines |
| Citations: | 37 - 6 self |
BibTeX
@ARTICLE{Ascher94stabilizationof,
author = {Uri M. Ascher and Hongsheng Chin and Linda R. Petzold and Sebastian Reich},
title = {Stabilization of constrained mechanical systems with DAEs and invariant manifolds},
journal = {J. Mech. Struct. Machines},
year = {1994},
volume = {23},
pages = {135--157}
}
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Abstract
Many methods have been proposed for the simulation of constrained mechanical systems. The most obvious methods have mild instabilities and drift problems, and consequently stabilization techniques have been proposed. A popular stabilization method is Baumgarte's technique, but the choice of parameters to make it robust has been unclear in practice. Here we first review some of the simulation methods which have been proposed and used in computations from a stability point of view. This involves concepts of differential-algebraic equations (DAE) and ODE invariants. We explain why Baumgarte's method may run into trouble, and why a further quest for finding better parameter values for this method will always remain frustrating. We then show how to improve it. We propose an efficient stabilization technique which may employ explicit ODE solvers in case of nonstiff or highly oscillatory problems and relates to coordinate projection methods. Examples of a two-link planar robotic arm and a squ...
