Work-conjugacy between rotation-dependent moments and finite rotations

In this paper we investigate the work-conjugacy between rotation-dependent moments and finite rotation measures. The methodology adopted consists of writing all the relevant quantities in terms of the rotation vector, using expressions that remain exact in the finite rotation range. Through this procedure, we show how (i) to identify work-conjugate (rotationdependent) moments and rotation measures, (ii) to derive a necessary condition for moment conservativeness and (iii) to obtain the general form of an isotropic conservative rotation-dependent moment. Several moment and finite rotation definitions that have been used in the past are investigated and, in particular, it is shown that the various existing definitions for the so-called semi-tangential moments are distinct in the finite rotation range and that not all of them are conservative. The tangent operator symmetry is discussed in the context of finite element analysis of conservative systems with rotational degrees of freedom, adopting either an additive or a multiplicative update.