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 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.