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Preprint 742-2002

Regularization of nonlinear equations of motion of multibody systems by index reduction with preserving the solution manifold

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Author(s) : Andreas Steinbrecher

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 742-2002

MSC 2000

70E55 Dynamics of multibody systems
65L80 Methods for differential-algebraic equations

Abstract :
Different types of solution behavior for equations of motion of multibody systems with respect to deviate from the solution manifold and numerical instabilities are considered.
An algorithm is presented that reduces the index of linear and nonlinear equations of motion of multibody systems in the usually used form by preserving all information about the solution manifold. The reduction is obtained by analyzing only the constraint matrix, the mass matrix and the transformation matrix. This technique allows the construction of a strangeness-free form which is suitable for numerical integration using stiff ODE solvers.
The here presented algorithm is the generalization of the already developed algorithm for linear equations of motion.
The obtained results are illustrated by a numerical example.

Keywords : multibody systems, equations of motion, solution manifold, deviation, index reduction, strangeness

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