A rotation matrix R with respect to a reference frame is used to describe certain crystal orientation. The logarithm of R, in 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 in 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.
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