New methods for modeling of the essentially nonlinear systems

The monograph presents a new approach to modeling and studying dynamic processes in the simplest two-link systems, where the input and output connections are somehow connected or interact with each other. It is shown that, neglecting nonlinearities, these systems can be described by analogous differential equations. The new method explicitly takes into account fluctuations in the speed of movement and tension. Using the Laplace transformations allowed us to derive equations describing the dynamics in a more general form. In this case, the elasticity of the system was considered as a function depending, in addition to the line parameters, on the oscillation frequency, which under certain conditions may lead to loss of stability. The theory of stability of open-loop systems with distributed parameters is obtained. For the cases of using internal feedbacks on the intermediate coordinate (pressure, voltage), a new frequency method for estimating stability was developed. The book contains new numerical methods based on the Runge-Kutta method, which made it possible to accurately simulate dynamic processes in nonlinear systems with lumped and distributed parameters.