An Overview of Methods for the Description of Rotations

Rotations in three dimensional space can be described by using different concepts, such as rotation tensors, attitude matrices, Euler angles, Rodrigues parameters or quaternions. In this paper the most common ones are presented mathematically and discussed with their advantages and disadvantages. Rotation tensors, Euler angles and quaternions are analyzed by consideration of in-orbit satellite control. Due to the numerous possibilities and the additional options for active and passive description, as well as intrinsic or extrinsic representations of the rotations, the description of the rotation is in many cases confusing. This work explains when it is appropriate to use each type of description, whether it concerns parametrization or the choice of an active or passive description of the rotations.