(1) The Institute of Applied Astronomy, St. Petersburg, Russia
(2) The Institute of Theoretical Astronomy, St. Petersburg, Russia
Currently employed solution for the Earth's rotation problem is valid for restricted intervals of time. It is based on the analytical theories of motion of the major planets involving not only trigonometric but also power and mixed terms with respect to time. Therefore, the expressions for the angles of precession and nutation contain such terms as well. For the rigid-body Earth's model such terms are due only to the adopted mathematical form of the solution. A successful attempt to represent the precession in the pure trigonometric form was made by Sharaf and Budnikova (Bull. ITA, 11, 231, 1967) with the aid of the linear trigonometric theory of the secular perturbations of the major planets.
In the present paper the equations of the translatory motion of the major planets and the Moon and the Poisson equations of the 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 is presented by means of the series in powers of the evolutionary variables with quasi-periodic coefficients. These series are constructed with the aid of a specialized Poisson series processor described in (T.V.Ivanova, IAU Symposium No. 172, 1995, in press). The behaviour of the evolutionary variables is governed by the secular system. Such representation of the Earth's rotation consistent with the general planetary theory (V.A.Brumberg, Analytical Techniques of Celestial Mechanica, Springer, Heidelberg, 1995) is valid for long intervals of time.