This monograph addresses the systematic representation of the methods of analysis developed by the authors as applied to such systems. Particular features of dynamic processes in such systems are studied. Special attention is given to an analysis of different resonant phenomena taking unusual and diverse forms.

Among the wide variety of nonlinear mechanical systems, it appears possible to distinguish a representative class which may be characterized by the presence of threshold nonlinear positional forces. Such systems demonstrate a sudden change in the behavior of elastic and dissipative forces. This monograph addresses the systematic representation of the new methods of analysis developed by the authors recently as applied to such systems. Specific features of dynamic processes of these systems are studied. Special attention is given to an analysis of different resonant phenomena taking unusual and diverse forms. These methods are applied to the analysis of mechanical systems designed for the generation and transformation of intensive processing of an impulsive nature. These are machines for rock fragmentation, impact processing, special types of shock testing machines and many other types of machinery.