AN Study of Polar Movement Using Continuous Mathematical Functions

Geodesy is a science that is related to determining the shape and geometry of the Earth and coordinates of points on the surface of, and above, the Earth, such as satellites and other moving objects above the Earth's surface. Therefore, in order to meet the geodesic goals in regards to positioning, we first need to define the geodesic-related coordinate system. In order to be able to objectify a point in three-dimensional space and to express its relation to a reference system called the coordinate system, we need to specify three parameters: 1 - origin 2 - axis directions 3 - parameters defining the position of a point in the coordinates system. One of the systems used in geodesy is the geocentric coordinate system, the origin of which is a point near the center of the Earth and the Z axis of the system is along the Earth's axis of rotation. Since the Earth's rotation is around the pole and the location of the pole is variable, the Z axis will have a different position, therefore we find it difficult to find the parameters determining a certain position in this system (factor III of the definition of the coordinate system). In this paper, using observations regarding the x, y components of the pole from 1962 to 1997, it can be concluded that this non-periodic motion can be studied and even predicted by using mathematical methods through the fitting of continuous functions. The results show that the power of showing this important movement in various mathematical functions is different, so that in some mathematical functions, the polar motion has an incremental acceleration, while others show that this movement has a completely irregular acceleration.