Колебания нелинейных систем

Currently, many different applied methods have been developed for studying the oscillations of nonlinear systems, which often have different mathematical designs and are not externally related to each other. However, it turns out that with the help of one class of integral equations these methods can be considered from a single point of view. This book is mainly devoted to the systematic consideration of some applied problems of the theory of nonlinear oscillations using the method of integral equations. In this way, it is possible, in particular, to establish a close connection between classical small parameter methods and methods for studying nonlinear automatic control systems based on the so-called filter hypothesis, as well as to give the latter a rigorous justification. In this case, it becomes possible to establish the range of applicability of various methods and give some effective estimates of the error of approximate solutions. All results obtained in this way are applicable to a wide class of systems described by nonlinear operator equations. The presented approach allows us to naturally introduce into the general theory of nonlinear oscillations very fruitful concepts that are widely used in the theory of automatic control, such as transfer functions, frequency characteristics, etc.
The book also discusses some issues of periodic oscillations not related to using integral equations.