Higher Order Nonlinear Systems

Abstract

The problem of extending phase-space techniques to Higher order nonline<-ix systems has been investigated in this dissertation. A new technique has been developed which is shown to be applicable to higher order nonlinear systems. The technique suggested is based on the f et that the higher order derivatives in a nonline it differential equation are related to the first order derivative through the slope of the phase trajectory (in the x-x plane) and its derivatives. In this technique, increment in the slope at the end of each small s ~ment of the trajectory is calculated and this j.ncr emental value is aided to the previous slope to gut a new value as the slope for the next trajectory s Oganent. The technique is discussed in detail and is illustrated with the help of a few exa~iiples of lineal, nonliiiear•, autonomous and nonaut. _onomous systeLn. The use of computer for this tecLriique is also discussed and a Flow chart for use in computer programme is g: ven. some new problems such as use of improved techniques for plotting are discussed briefly and it is hoped that further work in this direction will 1 ad to more worthwhile results.