Description of Changes in Crystal Orientations by the Elements of Logarithm of a Rotation Matrix

The logarithm ln⁡R of rotation matrix R is a skew symmetric tensor consisting of three independent elements of real numbers. In addition to the Euler angles and the axis/angle pair, the elements of ln⁡R called the log angles are also the set of three parameters of R. In this paper, we will show that...

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Detalles Bibliográficos
Autores principales: Onaka, Susumu, Hayashi, Kunio
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2017
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5662074/
https://www.ncbi.nlm.nih.gov/pubmed/29109815
http://dx.doi.org/10.1155/2017/4893956
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author Onaka, Susumu
Hayashi, Kunio
author_facet Onaka, Susumu
Hayashi, Kunio
author_sort Onaka, Susumu
collection PubMed
description The logarithm ln⁡R of rotation matrix R is a skew symmetric tensor consisting of three independent elements of real numbers. In addition to the Euler angles and the axis/angle pair, the elements of ln⁡R called the log angles are also the set of three parameters of R. In this paper, we will show that the concept of the log angles is also useful to discuss changes in crystal orientations. The changes in R as a function of the position are given by the changes in the log angles. As an example, orientation changes caused by arrays of dislocations in a plastically deformed Cu single crystal are discussed.
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spelling pubmed-56620742017-11-06 Description of Changes in Crystal Orientations by the Elements of Logarithm of a Rotation Matrix Onaka, Susumu Hayashi, Kunio Scanning Research Article The logarithm ln⁡R of rotation matrix R is a skew symmetric tensor consisting of three independent elements of real numbers. In addition to the Euler angles and the axis/angle pair, the elements of ln⁡R called the log angles are also the set of three parameters of R. In this paper, we will show that the concept of the log angles is also useful to discuss changes in crystal orientations. The changes in R as a function of the position are given by the changes in the log angles. As an example, orientation changes caused by arrays of dislocations in a plastically deformed Cu single crystal are discussed. Hindawi Publishing Corporation 2017-01-11 /pmc/articles/PMC5662074/ /pubmed/29109815 http://dx.doi.org/10.1155/2017/4893956 Text en Copyright © 2017 Susumu Onaka and Kunio Hayashi. https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Onaka, Susumu
Hayashi, Kunio
Description of Changes in Crystal Orientations by the Elements of Logarithm of a Rotation Matrix
title Description of Changes in Crystal Orientations by the Elements of Logarithm of a Rotation Matrix
title_full Description of Changes in Crystal Orientations by the Elements of Logarithm of a Rotation Matrix
title_fullStr Description of Changes in Crystal Orientations by the Elements of Logarithm of a Rotation Matrix
title_full_unstemmed Description of Changes in Crystal Orientations by the Elements of Logarithm of a Rotation Matrix
title_short Description of Changes in Crystal Orientations by the Elements of Logarithm of a Rotation Matrix
title_sort description of changes in crystal orientations by the elements of logarithm of a rotation matrix
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5662074/
https://www.ncbi.nlm.nih.gov/pubmed/29109815
http://dx.doi.org/10.1155/2017/4893956
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