| Summary: | At present, the study of the Earth and its geometry is of great interest to researchers in various fields of science. A number of studies concerning the Earth motion relative to the center of mass have been carried out. Methods of theoretical and celestial mechanics and mathematical statistics are used to prove that in the main approximation the Earth motion relative to the center of mass - the oscillation of the pole - is the union of two circles with a slow trend of the average position corresponding to the annual and the Chandler components.The article analyses the existing mathematical model (MM) of the oscillation process of the Earth's pole relative to the center of mass. The relationships of the Earth's pole oscillations relative to the center of mass with time are described by solving the Euler — Liouville differential equations of the celestial mechanics. The unknown coefficients in the equations are found using the numerical least-squares method by processing the daily data from the International Earth Rotation Service (IERS). It was noted that the examined MM does not allow observational data of the IERS to describe adequately the process of oscillations of the Earth's pole for a long time interval (up to 10 years), the discrepancy reaches 20%.For the first time, a method for describing and predicting the coordinates of the Earth's pole with time has been proposed using the Takagi — Sugeno fuzzy logic method. The developed method was tested for adequacy with the discrepancy of 4% at most over the entire time interval. An approach is proposed to describe the change in the coordinates of the Earth's pole using the first seven terms of the Weierstrass function series. The proposed method has a relatively high discrepancy with the IERS data (from 5 to 50%), but it allows us to describe the process of oscillations of the Earth's pole, as well as the method based on the Takagi — Sugeno fuzzy logic method over a long time interval.
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