Gristchak D. Mathematical models for nonlinear dynamics of airspace systems on the basis of hybrid asymptotic methods

On the basis of hybrid asymptotic approach a new mathematical models with analytical and numerical algorithms for the study and visualization of dynamic processes are proposed. An approximate analytical solutions of problems, which are described by singular differential equations with variable coefficients and their systems are obtained, in particular, the nonlinear dynamics of the rotating oscillator of variable length and mass; nonlinear vibrations of a satellite which moves in a plane of elliptical orbit; nonlinear dynamics and damping of the aircraft close to the perturbed surface; the dynamics of a rocket model with a concentrated moving at a given speed the time-dependent mass with visualization of the dynamic process depending on the specified motion parameters. In the application of a hybrid asymptotic approach the idea of combining the proposed approximate analytical solutions of nonlinear problems of dynamics with the use of existing software systems and the visualization of dynamic processes was further developed. The efficiency of the obtained approximate analytical solutions compared with the direct numerical method of the study. The research results are embedded in the practice of the Yuzhnoye State Design Office and educational process of Zaporizhzhia National University.