On the analysis of linear and nonlinear dynamical systems from transient-response data

Abstract

A general theory of the so-called "equations-of-motion" methods for the analysis of linear dynamical systems is developed first.It is then shown that when viewed from this general point of vantage, all of these linear methods can be extended in a straightforward manner to apply.to the analysis of nonlinear systems.In addition, through use of this theory, a new method is derived.It is essentially a variation of the well-known "Fourier transform" method for the analysis of linear systems but possesses certain advantages over previous methods.Application and effectiveness of this method are demonstrated by three examples, two of which are nonlinear -one highly so -and the third being of the fourth order.