On three-dimensional rotations, coordinate frames, and canonicalforms for it all

Some properties of the eigenproblem for a three-dimensional rotation matrix are shown, and related to the geometrical rotation parameters. The problem of assigning a unique canonical coordinate frame to a set of three mutually orthogonal axes is considered. The assignment is such that it corresponds to a minimal overall rotation with respect to the reference system. It is noted that this problem is of interest for the unique and consistent labeling of the principal axes of various tensors related to physical properties of materials, and symmetric matrices that appear in various disciplines of engineering