Regularized numerical integration of multibody dynamics with the generalized alpha method*

Parida, Nigam Chandra and Raha, Soumyendu (2009) Regularized numerical integration of multibody dynamics with the generalized alpha method*. In: Applied Mathematics and Computation, 215 (3). pp. 1224-1243.

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Abstract

This paper discusses the consistent regularization property of the generalized α method when applied as an integrator to an initial value high index and singular differential-algebraic equation model of a multibody system. The regularization comes from within the discretization itself and the discretization remains consistent over the range of values the regularization parameter may take. The regularization involves increase of the smallest singular values of the ill-conditioned Jacobian of the discretization and is different from Baumgarte and similar techniques which tend to be inconsistent for poor choice of regularization parameter. This regularization also helps where pre-conditioning the Jacobian by scaling is of limited effect, for example, when the scleronomic constraints contain multiple closed loops or singular configuration or when high index path constraints are present. The feed-forward control in Kane's equation models is additionally considered in the numerical examples to illustrate the effect of regularization. The discretization presented in this work is adopted to the first order DAE system (unlike the original method which is intended for second order systems) for its A-stability and same order of accuracy for positions and velocities.

Item Type:	Journal Article
Publication:	Applied Mathematics and Computation
Publisher:	Elsevier Science
Additional Information:	Copyright of this article belongs to Elsevier Science.
Keywords:	Numerical integration;Multi rigid body dynamics;High differential index;Differential-algebraic equations;Regularization
Department/Centre:	Division of Interdisciplinary Sciences > Supercomputer Education & Research Centre
Date Deposited:	16 Dec 2009 07:29
Last Modified:	19 Sep 2010 05:46
URI:	http://eprints.iisc.ac.in/id/eprint/23489

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