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
    Country/TerritorySweden
    CityLund
    Period25/10/201226/10/2012

    Keywords

    • Finite rotations
    • Quaternion parameters
    • Conservative integration

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