Institute of Theoretical Astronoy, St. Petersburg, Russia
Dynamics of the rotational motion of the Earth and Moon is investigated numerically. Very convenient Rodriges-Hamilton parameters are used for high-precision numerical integration of the rotational motion equations in the post-newtonian approximation over 600 yr time interval. The results of the numerical solution of the problem are compared with the contemporary analytical theories of the Earth's and Moon's rotation. The analytical theory of the Earth's rotation is compiled by the precession theory (Lieske et al., 1977), nutation theory (Souchay and Kinoshita, 1995) and geodesic nutation solution (Fukushima, 1991). The analytical theory of the Moon's rotation consists of the so-called Cassini's relations and the analytical solutions of the lunar physical libration problem (Moons, 1982), (Moons, 1984), (Moons, 1985), (Pesek, 1987). The comparisons reveal residuals both of periodic and systematic character. The values of systematic trends, as well as amplitudes of the largest long-periodic harmonics, are determined by means of a least-squares adjustment of the residual totality spanning 600 yr time interval. All the secular and periodic terms representing the residuals behavior are interpreted as the corrections to the mentioned analytical theories. In particular, the secular rate of the luni-solar inclination of the ecliptic to the equator J2000.0 ( -0".027, with a mean square error 0".000005) is very close to its theoretical value (Williams, 1994). It seems evident that the presence of the secular trends in the residuals of the proper rotation angles testifies the necessity of the introduction into the mathematical models, describing the rotations of the Earth and Moon, the terms simulating the tidal deceleration of the angular velocity.