A Melnikov method for strongly odd nonlinear oscillators

Abstract

In this paper. explicit calculations that extend the applicability of the Melnikov method to include strongly odd nonlinear and large forcing amplitude oscillating systems, are presented. We consider the response of the strongly nonlinear oscillating system governed by an equation of motion containing a parameter epsilon which need not be small. Phenomena considered are steady state response of strongly nonlinear oscillators subject to harmonic excitation. Two examples are given, they are the strongly nonlinear Duffing's equation and a pendulum suspended on a rotating arm. Finally, a adjustable factor is used to fit the simulation data. The theoretical chaotic behavior regions thus defined and plotted in the forcing amplitude versus parameter plane give the lower bounds for the true chaotic motion zones.