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On representing rotations by Rodrigues parameters in non-orthonormal reference systems.

A Morawiec1

  • 1Polish Academy of Sciences, Institute of Metallurgy and Materials Science, Reymonta 25, 30-059, Kraków, Poland.

Acta Crystallographica. Section A, Foundations and Advances
|September 1, 2016
PubMed
Summary
This summary is machine-generated.

This study extends Rodrigues parameters for analyzing polycrystalline materials, enabling direct application to non-orthogonal crystal lattice bases. This generalized approach simplifies crystallographic orientation mapping and analysis.

Keywords:
Rodrigues parametersframeslatticesquaternionsrotation representation

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Area of Science:

  • Crystallography
  • Materials Science
  • Computational Materials Science

Background:

  • Rodrigues vectors are commonly used for parameterizing rotations in 3D space.
  • Their application in analyzing orientation maps of polycrystalline materials is frequent due to their properties.
  • Conventional Rodrigues parameters are defined in orthonormal systems, posing challenges for non-orthogonal crystal lattices.

Purpose of the Study:

  • To extend the definition of Rodrigues parameters for direct application to non-Cartesian crystal lattice bases.
  • To develop a generalized formalism for crystallographic orientation analysis in oblique coordinate frames.
  • To enhance the applicability of Rodrigues parameters in materials science.

Main Methods:

  • Definition of generalized Rodrigues parameters as co- or contravariant vector components.
  • Development of a formalism compatible with arbitrary metric tensors of crystal lattices.
  • Adaptation of rotation composition and rotation matrix relationship formulas for generalized parameters.

Main Results:

  • Generalized Rodrigues parameters directly link to non-Cartesian crystal bases.
  • The formalism accommodates redundant crystallographic axes.
  • Rotation composition and matrix relationships are adapted for wider applicability, including arbitrary metric tensors.
  • The generalized parameters directly relate to rotation-invariant lattice directions and planes.

Conclusions:

  • The extended Rodrigues parameter formalism simplifies crystallographic orientation analysis in non-orthogonal systems.
  • This generalization enhances the utility of Rodrigues vectors for polycrystalline materials analysis.
  • The approach offers a more versatile and direct method for handling crystallographic orientations.