Specific features of dynamic interactions in nonlinear systems

Abstract

Specific features of nonlinear systems determined by the energy interaction of their coordinates are considered. To assess these features, the potential energy surfaces are considered, on which the system dynamics is presented using the trajectories of motion of an image point. The specific features of these trajectories are determined by the topological characteristics of the potential energy surface in the configuration space (local surface curvatures). Unlike linear systems, nonlinear systems are characterized by the presence on the energy surface of additional extremal curvatures and characteristic points: in addition to elliptic points, parabolic and hyperbolic points appear, which determine the character of geodetic lines near these extrema and points. The specific features of the geodetic lines determine the character of free and forced vibrations in the system, its dynamic features, and the presence of nonlinear effects in the system.