日本金属学会誌

J. Japan Inst. Met. Mater, Vol. 79, No. 1 (2015),
pp. 9-15

Log Angles: Characteristic Angles of Crystal Orientation Given by the Logarithm of Rotation Matrix

Kunio Hayashi1, Motoki Osada2, Yuki Kurosu1,∗, Yoji Miyajima1 and Susumu Onaka1

1Department of Materials Science and Engineering, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Yokohama 226-8502
2Department of Metallurgical Engineering, School of Engineering, Tokyo Institute of Technology, Tokyo 152-8552

Abstract:

A rotation matrix R with respect to a reference frame is used to describe certain crystal orientation. The logarithm of R, ln R is a skew symmetric tensor with three independent elements of real numbers. The goniometer-stage model in the present study shows that the three independent elements of ln R are the characteristic angles of R representing the rotation angles around coordinate axes. Different from various kinds of the Euler angles, the characteristic angles called the log angles are uniquely determined for certain R. [doi:10.2320/jinstmet.J2014036]


(Received 2014/8/25)

Keywords:

logarithm of matrix, misorientation, microstructure, Euler angles, axis/angle pair


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