The paper presents two novel second order conservative Lie-group geometric methods for integration of rigid body rotational dynamics. First proposed algorithm is a fully explicit scheme that exactly conserves spatial angular momentum of a free spinning body. The method is inspired by the Störmer–Verlet integration algorithm for solving ordinary differential equations (ODEs), which is also momentum conservative when dealing with ODEs in linear spaces but loses its conservative properties in a nonlinear regime, such as nonlinear SO(3) rotational group. Then, we proposed an algorithm that is an implicit integration scheme with a direct update in SO(3). The method is algorithmically designed to conserve exactly both of the two “main” motion integrals of a rotational rigid body, i.e., spatial angular momentum of a torque-free body as well as its kinetic energy. As it is shown in the paper, both methods also preserve Lagrangian top integrals of motion in a very good manner, and generally better than some of the most successful conservative schemes to which the proposed methods were compared within the presented numerical examples. The proposed schemes can be easily applied within the integration algorithms of the dynamics of general rigid body systems.
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September 2015
Research-Article
An Angular Momentum and Energy Conserving Lie-Group Integration Scheme for Rigid Body Rotational Dynamics Originating From Störmer–Verlet Algorithm
Zdravko Terze,
Zdravko Terze
Department of Aeronautical Engineering,
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: zdravko.terze@fsb.hr
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: zdravko.terze@fsb.hr
Search for other works by this author on:
Andreas Müller,
Andreas Müller
Institute for Robotics,
JKU Johannes Keppler University,
Altenbergerstraße 69,
Linz A-4040, Austria
e-mail: andreas.mueller@ieee.org
JKU Johannes Keppler University,
Altenbergerstraße 69,
Linz A-4040, Austria
e-mail: andreas.mueller@ieee.org
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Dario Zlatar
Dario Zlatar
Department of Aeronautical Engineering,
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: dario.zlatar@fsb.hr
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: dario.zlatar@fsb.hr
Search for other works by this author on:
Zdravko Terze
Department of Aeronautical Engineering,
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: zdravko.terze@fsb.hr
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: zdravko.terze@fsb.hr
Andreas Müller
Institute for Robotics,
JKU Johannes Keppler University,
Altenbergerstraße 69,
Linz A-4040, Austria
e-mail: andreas.mueller@ieee.org
JKU Johannes Keppler University,
Altenbergerstraße 69,
Linz A-4040, Austria
e-mail: andreas.mueller@ieee.org
Dario Zlatar
Department of Aeronautical Engineering,
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: dario.zlatar@fsb.hr
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: dario.zlatar@fsb.hr
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 22, 2014; final manuscript received September 24, 2014; published online April 2, 2015. Assoc. Editor: Dan Negrut.
J. Comput. Nonlinear Dynam. Sep 2015, 10(5): 051005 (11 pages)
Published Online: April 2, 2015
Article history
Received:
February 22, 2014
Revision Received:
September 24, 2014
Citation
Terze, Z., Müller, A., and Zlatar, D. (April 2, 2015). "An Angular Momentum and Energy Conserving Lie-Group Integration Scheme for Rigid Body Rotational Dynamics Originating From Störmer–Verlet Algorithm." ASME. J. Comput. Nonlinear Dynam. September 2015; 10(5): 051005. https://doi.org/10.1115/1.4028671
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