Construction of railway bogie motion nonlinear model and study of the stability of transverse vibrations taking into account external disturbances

The construction of nonlinear models of transport systems and the analysis of various types of stability of railway transport systems is an urgent scientific field related to traffic safety and the development of digital twins. Among the important problems it is necessary to highlight the construction of models taking into account the curvilinear rolling profile and external disturbances, as well as the study of the stability of solutions to nonlinear systems of differential equations modeling transverse vibrations of vehicles. The purpose of the article is to construct and study a generalized model of railway railway bogie motion using methods of motion stability theory. A generalization of the linear model of transverse vibrations of a railway bogie which takes into account the curvilinear rolling profile to the nonlinear case is proposed. The construction of a nonlinear model described by two second-order differential equations is considered and a transition to a system of four first-order differential equations in normal form is performed. The proposed model takes into account external perturbations described by nonlinear functions. These disturbances may have the character of external influences on the movement of a railway carriage, related to wind or seismic loads. Based on the first and second Lyapunov methods the stability conditions of the considered dynamic model of the transport system are obtained. The results can be used in solving problems related to ensuring stable modes of operation of transport systems, with the development of stability analysis algorithms for subsequent implementation in the form of a software package. The results are aimed at implementing models of rolling stock dynamics taking into account their use for the development of digital twins of transport infrastructure elements.