Approximate solution of a time-dependent differential equation

Abstract

In this paper an asymptotic analytic solving method for a differential equation with complex function, small nonlinearity and a slow variable parameter is developed. The procedure is an extension of the well known Bogolubov-Mitropolski method. The correctness of the procedure is proved by an example. The vibrations of a rotor on which a thin band is wound and on which a small linear damping acts are obtained. The analytical solutions are compared with numerical ones. They are in good agreement. © 1995 Kluwer Academic Publishers.