A supplementary note on constructing the general Earth's rotation theory

Representing a post-scriptum supplementary to a previous paper of the authors Brumberg & Ivanova (2011) this note aims to simplify the practical development of the Earth's rotation theory, in the framework of the general planetary theory, avoiding the non-physical secular terms and involving the separation of the fast and slow angular variables, both for planetary-lunar motion and Earth's rotation. In this combined treatment of motion and rotation, the fast angular terms are related to the mean orbital longitudes of the bodies, the diurnal and Euler rotations of the Earth. The slow angular terms are due to the motions of pericenters and nodes, as well as the precession of the Earth. The combined system of the equations of motion for the principal planets and the Moon and the equations of the Earth's rotation is reduced to the autonomous secular system with theoretically possible solution in a trigonometric form. In the above-mentioned paper, the Earth's rotation has been treated in Euler parameters. The trivial change of the Euler parameters to their small declinations from some nominal values may improve the practical efficiency of the normalization of the Earth's rotation equations. This technique may be applied to any three-axial rigid planet. The initial terms of the corresponding expansions are given in the Appendix.