A conservative quaternion-based time integration algorithm for rigid body rotations with implicit constraints

Martin Bjerre Nielsen, Steen Krenk

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Abstract

A conservative time integration algorithm for rigid body rotations is presented in a purely algebraic form in terms of the four quaternions components and the four conjugate momentum variables via Hamilton’s equations. The introduction of an extended mass matrix leads to a symmetric set of eight state-space equations where constraints are embedded without explicit use of Lagrange multipliers. The algorithm is developed by forming a finite increment of the Hamiltonian, which defines the proper selection of increments and mean values that leads to conservation of energy and momentum. The accuracy and conservation properties are illustrated by examples.
Original languageEnglish
Title of host publicationProceedings of the 25th Nordic Seminar on Computational Mechanics
EditorsK. Persson, J. Revstedt, G. Sandberg, M. Wallin
Number of pages4
PublisherLund University Faculty of Engineering
Publication date2012
ISBN (Print)978-91-7473-456-0
Publication statusPublished - 2012
EventNSCM25: 25th Nordic Seminar on Computational Mechanics - University of Lund, Lund, Sweden
Duration: 25 Oct 201226 Oct 2012

Conference

ConferenceNSCM25
LocationUniversity of Lund
CountrySweden
CityLund
Period25/10/201226/10/2012

Keywords

  • Finite rotations
  • Quaternion parameters
  • Conservative integration

Cite this

Nielsen, M. B., & Krenk, S. (2012). A conservative quaternion-based time integration algorithm for rigid body rotations with implicit constraints. In K. Persson, J. Revstedt, G. Sandberg, & M. Wallin (Eds.), Proceedings of the 25th Nordic Seminar on Computational Mechanics Lund University Faculty of Engineering.