Premium
Simo–Vu Quoc rods using Clifford algebra
Author(s) -
McRobie F. A.,
Lasenby J.
Publication year - 1999
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19990610)45:4<377::aid-nme586>3.0.co;2-p
Subject(s) - algebra over a field , mathematics , lie algebra , euclidean space , dimension (graph theory) , lie group , geometric algebra , differential geometry , euclidean geometry , kinematics , symbolic computation , quaternion , clifford algebra , pure mathematics , mathematical analysis , geometry , physics , classical mechanics
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.