Modeling and velocity stabilization of constrained mechanical systems
type: Item
instance of: scholarly article
title: Modeling and velocity stabilization of constrained mechanical systems
zbMATH Open document ID: 0818.65072
DOI: 10.1007/BF01934263
author: Taifun Alishenas
author: Örn Ólafsson
published in: BIT
publication date: 1995-08-15T00:00:00Z
review text: The use of some one- and multistep methods for the numerical integration of constrained mechanical systems with and without stabilization is discussed in order to compare their efficiency. In particular, the use of (high-order) multistep methods is considered. A descriptor form of the differential algebraic equation (DAE) formulation is used and applied to two non-stiff test problems. By index reduction, the DAE model is transferred to an equivalent ordinary differential equation (ODE) representation whose unstable numerical solution is stabilized by projection back onto the constraint manifold. A perturbation analysis shows that velocity stabilization is the most efficient projection with regard to improvement of the numerical integration. How frequently the numerical solution of the transferred ODE should be stabilized is discussed. For a class of multistep methods, a strategy of stabilizing at certain time steps and performing a much less demanding quasi-stabilization at the others is suggested, especially for high-order methods. With these high-order methods, stabilization is not even necessary for the second test problem.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 70H03
zbMATH DE Number: 739433
zbMATH Keywords: multistep methods
zbMATH Keywords: constrained mechanical systems
zbMATH Keywords: stabilization
zbMATH Keywords: differential algebraic equation
zbMATH Keywords: index reduction
zbMATH Keywords: test problem
reviewed by: Stephen L. Campbell
describes a project that uses: Matlab
describes a project that uses: RODAS
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 739433