Some basic kinematical relations for finite deformations of continua

This paper summarizes a number of general kinematical identities developed by the authors in early 1981 for finite deformations of continua. Included are explicit relations between various spin tensors and the symmetric and antisymmetric parts of the velocity gradient, various material strain measures, and strain rates. These relations are expressed in the general, coordinate-independent form (which is the main contribution of this work), as well as in terms of their spectral components (due to Hill).