APPROXIMATE SOLUTION OF A TIME-DEPENDENT DIFFERENTIAL-EQUATION

In this paper an asymptotic analytic solving method for a differential equation with complex function, small nonlinearity and a slow variabl e parameter is developed. The procedure is an extension of the well kn own Bogolubov-Mitropolski method. The correctness of the procedure is proved by an example. The vibrations of a rotor on which a thin band i s wound and on which a small linear damping acts are obtained. The ana lytical solutions are compared with numerical ones. They are in good a greement.