Applications of the methods of averaging and successive approximations for studying nonlinear oscillations

Abstract

The question is examined of the existence of a solution of the Cauchy problem for a system of ordinary differential equations, standard in the sense of Bogoliubov /1 –3/, describing a wide class of nonlinear processes of oscillations and rotations. Constructive sufficient conditions for the existence and uniqueness of this solution on asymptotically large time intervals are established by the method of successive approximations /4,5/. Smoothness properties of a nonstationary process with respect to the problem parameters (initial data) are investigated.