Earth rotation equations containing both nutation and polar motion

The theory of Smith (1977, 1980) is generalized to include both forced and free rotations by introducing an arbitrarily rotating nutation frame. The Eulerien equations are transformed to include the following unknowns: the angular velocity of the nutation frame with respect to the spatial frame, which represents the nutation, and the angles defining the orientation of the Earth with respect to the nutation frame, which represents the polar motion. Together with the definition of the nutation frame (as the definition of the nutation frame is arbitrary to some extent), one can solve simultaneously forced and free nutation and polar motion. As demonstrative examples, studies of nutation and polar motion are made by assuming the nutation axis to be the Earth's figure axis, rotation axis and angular momentum axis respectively. And the case of the celestial ephemeris pole is also studied.