Asymptotic Method for Truly Non-linear Oscillator with Time Variable Parameter

Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovica 6, 21000 Novi Sad, Serbia

Abstract

In this paper a new analytical method for solving the truly (pure) non-linear differential equation with slow-time variable parameter is developed. The method is based on the solution of the corresponding differential equation with a constant parameter, where the exact frequency of vibration is introduced. The approximate solution of the differential equation with time variable parameter is assumed in the aforementioned form, but with time variable amplitude and phase. The solution of the differential equation is nonstationary with time variable amplitude and period of vibration. In the paper an example with linear time variable parameter and non-integer order non-linearity is considered. The obtained approximate solution of the differential equation is compared with an exact numerical one and shows good agreement.