On Asymptotic Solutions of Fourth Order Over- Damped Nonlinear Systems in Presence on Certain Damping Forces

Abstract

The nature of the solutions of the over-damped systems depends on the nature of damping forces. In this article, the Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended and modified for obtaining the solutions of fourth order overdamped nonlinear systems, when the damping force is such that, one of the eigenvalues of the linear systems is vanishes or tends to zero and the other eigenvalues are in integral multiple. The method is illustrated by an example. The solutions obtained by the presented KBM method for different set of initial conditions show good coincidence with those obtained by the numerical method