Stabilization of constrained mechanical systems with DAEs and invariant manifolds

  • Many methods have been proposed for the simulation of constrained mechanical systems. The most obvious of these have mild instabilities and drift problems. 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. Some of the simulation methods that have been proposed and used in computations are reviewed here, from a stability point of view. This involves concepts of differential-algebraic equation (DAE) and ordinary differential equation (ODE) invariants. An explanation of the difficulties that may be encountered using Baumgarte's method is given, and a discussion of why a further quest for better parameter values for this method will always remain frustrating is presented. It is then shown how Baumgarte's method can be improved. An efficient stabilization technique is proposed, which may employ explicit ODE solvers in case of nonstiff or highly oscillatory problems and which relates to coordinate proMany methods have been proposed for the simulation of constrained mechanical systems. The most obvious of these have mild instabilities and drift problems. 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. Some of the simulation methods that have been proposed and used in computations are reviewed here, from a stability point of view. This involves concepts of differential-algebraic equation (DAE) and ordinary differential equation (ODE) invariants. An explanation of the difficulties that may be encountered using Baumgarte's method is given, and a discussion of why a further quest for better parameter values for this method will always remain frustrating is presented. It is then shown how Baumgarte's method can be improved. An efficient stabilization technique is proposed, which may employ explicit ODE solvers in case of nonstiff or highly oscillatory problems and which relates to coordinate projection methods. Examples of a two-link planar robotic arm and a squeezing mechanism illustrate the effectiveness of this new stabilization method.show moreshow less

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Metadaten
Author:Uri M. Ascher, Hongsheng Chin, Linda R. Petzold, Sebastian Reich
URN:urn:nbn:de:kobv:517-opus-15698
Series (Serial Number):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe, ISSN 1866-8372 (paper 033)
Document Type:Postprint
Language:English
Date of Publication (online):2007/11/21
Year of Completion:1994
Publishing Institution:Universität Potsdam
Release Date:2007/11/21
Source:Mechanics Based Design of Structures and Machines. - ISSN 1539-7742. - 23 (1995), p. 135 - 157
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Extern / Extern
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Notes extern:
This is an electronic version of an article published in Mechanics Based Design of Structures and Machines, Volume 23, Issue 2 1995 , pages 135 - 157.
Mechanics Based Design of Structures and Machines is available online at informaworldTM .