Simo-Vu Quoc rods using Clifford algebra

We present an alternative derivation of Simo and Vu Quocʹs numerical algorithm1 for modelling the non-linear dynamic behaviour of rods. The original derivation uses di erential 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 Cli ord or geometric algebra as developed by Hestenes2; 3 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.