A celestial mechanics model of the Earth’s rotation irregularity

A mathematical model of perturbed rotational motions of the deformable Earth, adequate to astrometric measurements of the International Earth Rotation Service (IERS), is constructed using methods of celestial mechanics. It is based on the gravitational tidal mechanism of the influence of the Sun and Moon. The authors have found fine resonant structure of interaction of long-period zonal tides (annual, semi-annual, monthly, and two-week) with diurnal and semidiurnal tides. This essential property is reliably confirmed by spectral analysis of the IERS data. In this paper, a numerical simulation of tidal irregularities of the Earth’s axial rotation is performed. The primary emphasis is placed on the analysis of variations of the duration of the day on short time intervals with periods of one year and less (intra-annual oscillations) and their forecast.