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

Publication: Research - peer-reviewArticle in proceedings – Annual report year: 2012

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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
StatePublished

Conference

ConferenceNSCM25
CountrySweden
CityLund
Period25/10/1226/10/12

Keywords

  • Finite rotations, Quaternion parameters, Conservative integration
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