A METHOD FOR ANALYZING THE RESONANCE MOTION OF A NONLINEAR OSCILLATORY SYSTEM

A method for analyzing the resonance motion of a nonlinear oscillatory system of differentia] equations with slowly varying parameters is considered. To analyze the resonance motion, the system is reduced to the singular perturbed form and then the method of integral manifolds is used to reduce the order of the system. The equations of motion of the system on the integral manifold are close to the equations of a nonlinear "pendulum." The further investigation of the resonance (the analysis of the existence and stability of the durable resonance mode) involves the analysis of solutions to the equations of the perturbed motion of the pendulum on the integral manifold. The method suggested is applied to the analysis of a nonlinear resonance in [he motion of a rigid body in the atmosphere. This method is illustrated by characteristic numerical results.