Research Article

Simo–Vu Quoc rods using Clifford algebra

  1. F. A. McRobie*,
  2. J. Lasenby

Article first published online: 15 APR 1999

DOI: 10.1002/(SICI)1097-0207(19990610)45:4<377::AID-NME586>3.0.CO;2-P

Issue

International Journal for Numerical Methods in Engineering

International Journal for Numerical Methods in Engineering

Volume 45, Issue 4, pages 377–398, 10 June 1999

Additional Information

How to Cite

McRobie, F. A. and Lasenby, J. (1999), Simo–Vu Quoc rods using Clifford algebra. International Journal for Numerical Methods in Engineering, 45: 377–398. doi: 10.1002/(SICI)1097-0207(19990610)45:4<377::AID-NME586>3.0.CO;2-P

Author Information

  1. Cambridge University Engineering Department, Trumpington St., Cambridge, CB2 1PZ, U.K.

*Department of Engineering, Cambridge University, Trumpington street, Cambridge CB2 lPZ, U.K.

Publication History

  1. Issue published online: 15 APR 1999
  2. Article first published online: 15 APR 1999
  3. Manuscript Revised: 21 JUL 1998
  4. Manuscript Received: 25 SEP 1997

Funded by

  • EPSRC Applied Nonlinear Mathematics Programme
  • Royal Society of London

SEARCH

SEARCH BY CITATION

ARTICLE TOOLS

Get PDF (145K)

Keywords:

  • Clifford algebra;
  • geometric algebra;
  • rods;
  • large rotations

Abstract

We present an alternative derivation of Simo and Vu Quoc's numerical algorithm for modelling the non-linear dynamic behaviour of rods. The original derivation uses differential topology, describing large rotations using the Lie group SO(3) and Lie algebra so(3), but resorting to quaternions for the numerical implementation. The new derivation uses Clifford or geometric algebra as developed by Hestenes for both formulation and implementation. We contend that the new approach is considerably simpler to follow, and thereby allows alternative modelling strategies to be more readily investigated. The new description is also novel in that all formulae for rotational kinematics are applicable in a Euclidean space of any dimension. Copyright © 1999 John Wiley & Sons, Ltd.

Get PDF (145K)