Application of the field method to the non-linear theory of vibrations

This paper deals with the generalization of the field method to weakly non-linear vibrational systems with one degree of freedom. The field co-ordinate and field momentum approaches are combined with the method of multiple time scales in order to obtain the amplitude and phase of oscillations in the first approximation. Apart from the fact that the algorithm of obtaining motion is condensed for the cases of a free vibrational system and system with slowly varying parameters, in this paper the field method is extended to a parametrically excited system and system with external excitation.