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IssuesArchive of Issues2006-3pp.23-33

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S. E. Perelyaev, "On the global parametrizations of a group of 3D rotations," Mech. Solids. 41 (3), 23-33 (2006)
Year 2006 Volume 41 Number 3 Pages 23-33
Title On the global parametrizations of a group of 3D rotations
Author(s) S. E. Perelyaev (Moscow)
Abstract Basic methods of the introduction of a global bijective parametrization of the space of rigid body rotations are described and characterized (from the mathematical point of view, these are methods of the embedding of the group SO(3) into Rn). In addition to the well-known methods of nine-dimensional (using the matrix of direction cosines) and six-dimensional (using two columns of this matrix) parametrizations, a modified six-dimensional parametrization necessary for the description of the scarcely known five-dimensional Hopf parametrization is introduced and analyzed. A comparative analysis of different approaches to the global bijective parametrization of the group SO(3) is carried out.
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Received 24 March 2004
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