AbstractDynamics of the rotational motion of the Earth and Moon is investigated numerically. Very convenient Rodrigues-Hamilton parameters are used for high-precision numerical integration of the rotational motion equations in the post-newtonian approximation over a 400 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 composed of the precession theory (Lieske et al., 1977), nutation theory (Souchay and Kinoshita, 1996) and geodesic nutation solution (Fukushima, 1991). The analytical theory of the Moon’s rotation consists of the so-called Cassini relations and the analytical solutions of the lunar physical libration problem (Moons, 1982), (Moons, 1984), (Pešek, 1982). The comparisons reveal residuals both of periodic and systematic character. All the secular and periodic terms representing the behavior of the residuals are interpreted as corrections to the mentioned analytical theories. In particular, the secular rate of the luni-solar inclination of the ecliptic to the equator J2000.0 (–0027, with a mean square error 0000005) is very close to its theoretical value (Williams, 1994).
