TY  - GEN
A1  - Ascher, Uri M.
A1  - Chin, Hongsheng
A1  - Petzold, Linda R.
A1  - Reich, Sebastian
T1  - Stabilization of constrained mechanical systems with DAEs and invariant manifolds
N2  - 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 projection methods. Examples of a two-link planar robotic arm and a squeezing mechanism illustrate the effectiveness of this new stabilization method.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 033 
Y1  - 2007
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/1447
UR  - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-15698
ER  -