Geodetic data and their subsequent statistical analysis enable mathematical modeling and identifying the stress-deformed state of geodynamic systems in concern to the aspect of natural and man-made disasters prediction. Geodetic monitoring geodynamic processes is necessary for solving a number of scientific and practical tasks of geodesy i.e. expanding and maintaining the national geodetic network, studying changes in gravity field in time, using GNSS technology. Most important extension of research is mathematical modelling of geodynamic systems in a predictive order. To study the complex (nonlinear) geodynamic processes the appropriate mathematical framework should be selected. Here are theoretical foundations for studying rotation movements of the earth’s surface. A mathematical model of rotary circular structures of the Earth was mentioned. There are mathematical models explaining the nature of sudden global, regional and some local geodynamic processes. They are based on differences in temporal and spatial scales, of geodynamic systems. Theoretical bases of description rotational motions on a plane by a system of differential equations were considered. Some examples of integral curves were given. They can be qualitative characteristics of geodynamic systems. In many cases, a similar trajectory corresponds to the rotational horizontal movements of the earth’s surface.