Interaction of flows on quadrics

We interpret the Rodrigues formula describing a torsion of a rigid body in terms of Lie derivatives. We consider a more general situation where vector fields on quadrics (ellipsoids and hyperboloids) are dragged by other vector fields. The question is about the adjoint representation of a Lie group which is more general than the usual torsion group of the three-dimensional Euclidean space. © 2002 Plenum Publishing Corporation.