The rotation rate field and geometry of orientation space

This paper contains information about the Riemannian structure of orientation space which is necessary for the analysis of the rotation rate field, which in turn describes some aspects of the plastic deformation of textured polycrystalline materials. The components of the metric tensor and the connection coefficients in the coordinates used in quantitative texture analysis are given. The relation between the vector components at symmetrically equivalent points and the relation between the frequently used vectors of infinitesimal rotations are presented. The solution of the continuity equation is given for the case of a constant rotation rate field during the deformation process.