A note on the time dependence of the effective axis and angle of a rotation

Abstract

The time dependent rotation of one orthogonal coordinate system with respect to a fixed one is considered in the parametrization based on the effective axis and angle of the rotation, a parametri zation which has recently been used to discuss the irreducible representations of the rotation group. The method of the intrinsic vector is used to derive the equations of motion fur the instantaneous effective axis and angle. A new representation of the angular velocity is obtained in a rotating or· thogonal coordinate system generated by a unit vector along the effective axis, and a new geometrical interpretation of the effective angle is given.