Title :
On three-dimensional rotations, coordinate frames, and canonical forms for it all
Author :
Verriest, Erik I.
Author_Institution :
Sch. of Electr. Eng., Georgia Inst. of Technol., Atlanta, GA, USA
fDate :
10/1/1988 12:00:00 AM
Abstract :
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
Keywords :
eigenvalues and eigenfunctions; matrix algebra; canonical forms; coordinate frames; eigenproblem; minimal overall rotation; mutually orthogonal axes; rotation matrix; symmetric matrices; three-dimensional rotations; Coaxial components; Elasticity; Electrons; Labeling; Radar; Robot kinematics; Sonar; Symmetric matrices; Tensile stress; Transmission line matrix methods;
Journal_Title :
Proceedings of the IEEE
