An equivalent nonlinearization method for strongly nonlinear oscillations

An equivalent nonlinearization method is proposed for the study of certain kinds of strongly nonlinear oscillators. This method is to express the nonlinear restored force of an oscillatory system by a polynomial of degree two or three such that the asymptotic solutions can be derived in terms of elliptic functions. The least squares method is used to determine the coefficients of approximate polynomials. The advantage of present method is that it is valid for relatively large oscillations. As an application, a strongly nonlinear oscillator with slowly varying parameters resulted from free-electron laser is studied in detail. Comparisons are made with other methods to assess the accuracy of the present method.