The use of the quaternions for describing the Earth’s rotation

We derive the quaternions expressing the rotation transformation between celestial and terrestrial reference systems as functions of the parameters giving the position of the Celestial Intermediate Pole (CIP) in those two systems, and of the rotation angle. A first version is associated with the common Earth Orientation Parameters (EOP) recommended by the International Earth Rotation and Reference System Service (IERS) and IAU; a second version uses the direction cosines of the CIP in the International Terrestrial Reference System (ITRS) instead of the conventional pole coordinates. Whereas matrix and quaternion methods are numerically comparable, the quaternion formulation offers a very elegant and concise analytical representation, that does not exist for Earth rotation matrix and that can be easily programmed. In our view, this quaternion representation reinforces the scope of the nowadays parameters adopted for describing Earth rotation.