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The rotation rate field and geometry of orientation space
Author(s) -
Morawiec A.
Publication year - 1990
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s002188989000512x
Subject(s) - rotation (mathematics) , orientation (vector space) , geometry , infinitesimal , field (mathematics) , mathematics , tensor (intrinsic definition) , mathematical analysis , connection (principal bundle) , deformation (meteorology) , vector field , metric (unit) , physics , pure mathematics , operations management , meteorology , economics
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.