A study was conducted to demonstrate amplitude and frequency analysis of diurnal oscillations of the Earth's pole. The amplitudes and frequencies of diurnal oscillations due to gravitational tidal solar and lunar torques were analyzed in terms of the model with a few parameters in the framework of classical mechanics. The structural properties of diurnal oscillations of the pole coordinates were derived from the dynamic Euler-Liouville equations taking into account irregular perturbations. The results obtained from the model of the Earth's polar motion were compared with high-precision very-long baseline interferometry (VLBI) on a short time scale. It was necessary to solve a fundamental problem involving the construction of dynamic models of the Earth's rotary-oscillatory motions consistent with the observed and measured data of the International Earth Rotation Service (IERS) to provide accurate coordinates and time moments for ground-based objects and for those moving in near-Earth space.
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