DocumentCode
938075
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
Volume
76
Issue
10
fYear
1988
fDate
10/1/1988 12:00:00 AM
Firstpage
1376
Lastpage
1378
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;
fLanguage
English
Journal_Title
Proceedings of the IEEE
Publisher
ieee
ISSN
0018-9219
Type
jour
DOI
10.1109/5.16335
Filename
16335
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