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Is There an Optimal Choice of Configuration Space for Lie Group Integration Schemes Applied to Constrained MBS?

[+] Author Affiliations
Andreas Müller

Institute of Mechatronics, Chemnitz, Germany

Zdravko Terze

University of Zagreb, Zagreb, Croatia

Paper No. DETC2013-12151, pp. V07AT10A020; 10 pages
doi:10.1115/DETC2013-12151
From:
  • ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 7A: 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Portland, Oregon, USA, August 4–7, 2013
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5596-6
  • Copyright © 2013 by ASME

abstract

Recently various numerical integration schemes have been proposed for numerically simulating the dynamics of constrained multibody systems (MBS) operating. These integration schemes operate directly on the MBS configuration space considered as a Lie group. For discrete spatial mechanical systems there are two Lie group that can be used as configuration space: SE(3) and SO(3) × ℝ3. Since the performance of the numerical integration scheme clearly depends on the underlying configuration space it is important to analyze the effect of using either variant. For constrained MBS a crucial aspect is the constraint satisfaction. In this paper the constraint violation observed for the two variants are investigated. It is concluded that the SE(3) formulation outperforms the SO(3) × ℝ3 formulation if the absolute motions of the rigid bodies, as part of a constrained MBS, belong to a motion subgroup. In all other cases both formulations are equivalent. In the latter cases the SO(3) × ℝ3 formulation should be used since the SE(3) formulation is numerically more complex, however.

Copyright © 2013 by ASME

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