AN ELLIPTIC PERTURBATION METHOD FOR CERTAIN STRONGLY NON-LINEAR OSCILLATORS

摘要

An elliptic perturbation method is presented for calculating periodic solutions of strongly non-linear oscillators of the form x double over dot + c(1)x + c(3)x(3) = epsilon f(x, x over dot), in which the Jacobian elliptic functions are employed instead of usual circular functions in the conventional perturbation procedure. Three types of Duffing-Van der Pol equation with f(x, x over dot) = (1 - x(2))x over dot are studied in detail. The present method can give a second approximate solution and therefore its accuracy is much higher than that of other methods in which the solutions are only first approximations. (C) 1996 Academic Press Limited [References: 17]