Log angles: Characteristic angles of crystal orientation given by the logarithm of rotation matrix

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.