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A New Theoretical and Numerical Approach to Finite Rigid Body Rotations Based on Lie Group Theory

[+] Author Affiliations
Sotirios Natsiavas, Elias Paraskevopoulos, Nikolaos Potosakis

Aristotle University, Thessaloniki, Greece

Paper No. DETC2013-12426, pp. V07AT10A026; 10 pages
doi:10.1115/DETC2013-12426
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

A systematic theoretical approach is presented first, in an effort to provide a complete and illuminating study on motion of a rigid body rotating about a fixed point. Since the configuration space of this motion is a differentiable manifold possessing group properties, this approach is based on some fundamental concepts of differential geometry. A key idea is the introduction of a canonical connection, matching the manifold and group properties of the configuration space. Next, following the selection of an appropriate metric, the dynamics is also carried over. The present approach is theoretically more demanding than the traditional treatments but brings substantial benefits. In particular, an elegant interpretation can be provided for all the quantities with fundamental importance in rigid body motion. It also leads to a correction of some misconceptions and geometrical inconsistencies in the field. Finally, it provides powerful insight and a strong basis for the development of efficient numerical techniques in problems involving large rotations. This is demonstrated by an example, including the basic characteristics of the class of systems examined.

Copyright © 2013 by ASME

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