Abstract. A hybrid transformation method is proposed for the problems of analyzing nonlinear dynamical sys-tems of polynomial structure. The method is based on polynomial transformations and allows for analyzing analytically the properties of stationary solutions for systems in normal and extreme operating conditions; for non-stationary (e.g., transition) solutions, it may be used in conjunction with the Runge-Kutta numerical method. The method has significantly less computational complexity than numerical methods of an equivalent degree of accuracy and does not require determination of conditions and domain of convergence of the approximate solution. It makes it possible to calculate characteristics of various technical objects under external periodic influences. As an example, the method of transformations is used to study a dynamic model of truck crane and to carry out the calculations for vibration-proof systems of boat motors.

Keywords: nonlinear differential equation, analytical method, polynomial transformation, stationary mode

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