Introduction

The introduction describes historical information about the state of the nonlinear theory of vibration-impact (strongly nonlinear) dynamic systems, and also lists numerous machines and mechanisms whose operation in industrial, civil, road, hydraulic, and other types of production is necessarily associated with impact interactions of elements. It is indicated that the volume of this work is so large that the problem of creating high-performance and reliable systems is extremely urgent. It is substantiated that the theoretical study of the nonlinear dynamics of multi-mass systems with impact interactions makes it natural to use the numerical and analytical method of point mappings of Poincaré surfaces. The main achievements in the theory of research of vibro-impact machines and mechanisms are presented. It is especially noted that the work was written in the traditions of the Nizhny Novgorod school of the theory of nonlinear oscillations—the school of Academician A.A. Andronov and presents the main results of the four chapters of the book.