Periodic solutions of strongly quadratic non-linear oscillators by the elliptic perturbation method

摘要

The elliptic perturbation method is applied to the study of the periodic solutions of strongly quadratic non-linear oscillators of the form (x) over tilde + c(1) x + c(2) x(2) = epsilon f(x, (x) over dot), in which the Jacobian elliptic functions are employed. The generalized Van der Pol equation with f(x, (x) over dot) = mu(0) + mu(1) x - mu(2) x(2) is Studied in detail. Comparisons are made with the solutions obtained by using the Lindstedt-Poincare method and Runge-Kutta method to show the efficiency of the present method. (C) 1998 Academic Press Limited. [References: 30]