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Störmer-Verlet Integration Scheme for Multibody System Dynamics in Lie-Group Setting

[+] Author Affiliations
Zdravko Terze, Dario Zlatar

University of Zagreb, Zagreb, Croatia

Andreas Mueller

Institute of Mechatronics, Chemnitz, Germany

Paper No. DETC2013-12308, pp. V07AT10A025; 7 pages
doi:10.1115/DETC2013-12308
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

Störmer-Verlet integration scheme has many attractive properties when dealing with ODE systems in linear spaces: it is explicit, 2nd order, linear/angular momentum preserving and it is symplectic for Hamiltonian systems. In this paper we investigate its application for numerical simulation of the multibody system dynamics (MBS) by formulating Störmer-Verlet algorithm for the rotational rigid body motion in Lie-group setting. Starting from the investigations on the single free rigid body rotational dynamics, the paper introduces modified RATTLE integration scheme with the direct SO(3) rotational update. Furthermore, non-canonical Lie-group Störmer-Verlet integration scheme is presented through the different derivation stages. Several presented numerical examples show excellent conservation properties of the proposed geometric algorithm.

Copyright © 2013 by ASME

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