Analytic Approximate Periodic Solutions Based on Harmonic Analysis

In the present paper we introduce an analytic approximation technique based on harmonic analysis for the solution of differential equations, and we apply this technique in two concrete cases. First we study the differential equation obtained by the law of electromagnetic induction for reluctance motors. The exact analytical solution of this equation can be determined only for a few particular cases. Our paper presents a method which gives a very good approximate analytical solution for the general case, together with its harmonics. Next we use the proposed technique to solve the problem of free oscillations of self-excited systems. While other analytical techniques used to solve this problem, such as perturbation-type methods, yield useful approximations only for small parameter values, the proposed method does not depend on the existence of small parameters in the considered nonlinear equations.