Energy Flow of Nonlinear Dynamical Systems

Abstract

This chapter gives the developed energy flow theory and approach for nonlinear dynamical systems defined by vector fields in phase space, which will be used in the following chapters of this monograph. The generalised potential energy and kinetic energy in phase space are defined, which are two scalar variables embedded into the phase space to investigate the energy flow behaviour of nonlinear dynamical systems. The first one involves positions of flow points in phase space and the second one links to the tangent vector, flow directions, in tangent bundle of vector fields.