Kyrkach K. Mathematical modeling of transient processes in nonlinear electromechanical systems by an operational method of S-transformations

Dissertational work is devoted to improvement of a method of nonclassical operational calculation for the solution of problems of the analysis of dynamic processes in nonlinear electrotechnical and mechanical systems, and also nonlinear systems of the fractional order. Analysis of approximation methods of modelling of transient processes in linear and nonlinear systems of the whole and fractional orders is made in work. The conclusion on absence of a united universal method of a finding approximation solutions of the nonlinear differential equations, suitable for the solution of problems with different types of nonlinearity is drawn. For the first time the method of nonclassical operational calculation to the analysis of processes in nonlinear electromechanical systems, and also systems of the fractional order is applied. Representation of the image of unknown function is obvious in the form of a vector of unknown coefficients allows to receive system of the nonlinear algebraic equations concerning unknown coefficients. The computing experiments allowing to compare the considered methods are made, analytical expressions of a trajectory of movement of the steam-ship are constructed, and some applied problems of the analysis of transient and oscillatory processes are solved.