NEW METHOD OF ANALYZING THE STABILITY AND PERIODIC OSCILLATION OF SECOND-ORDER NONLINEAR SYSTEMS.

This paper discusses the stability of second-order nonlinear systems and presents a new method of deriving an approximate periodic solution of the oscillatory system. The method of analyzing the stability is to associate the differential equation with a dynamical system and to discuss whether the energy of the point is increased or decreased by forced periodic oscillation. The new approximate method of analysis for periodic oscillation establishes an approximate expression for the energy of the point at each instant. This analytical method offers physical meaning in the determination, following an algorithm, of stability and an approximate periodic solution. The method also has the special feature that harmonic components can be obtained simultaneously by a single procedure.