On constructing the general Earth's rotation theory

V. A. Brumberg, T. V. Ivanova

Celestial Mechanics and Dynamical Astronomy, 109(4), 385-408 (2011)

Keywords: Earth’s rotation theory, Euler parameters, Secular system, General planetary theory

Abstract

In the present paper the equations of the orbital motion of the major planets and the Moon and the equations of the three–axial rigid Earth’s rotation in Euler parameters are reduced to the secular system describing the evolution of the planetary and lunar orbits (independent of the Earth’s rotation) and the evolution of the Earth’s rotation (depending on the planetary and lunar evolution). Hence, the theory of the Earth’s rotation can be presented by means of the series in powers of the evolutionary variables with quasi-periodic coefficients with respect to the planetary–lunar mean longitudes. This form of the Earth’s rotation problem is compatible with the general planetary theory involving the separation of the short–period and long–period variables and avoiding the appearance of the non–physical secular terms.