A PERTURBATION-ITERATIVE METHOD FOR DETERMINING LIMIT-CYCLES OF STRONGLY NONLINEAR OSCILLATORS

A perturbation-iterative method is presented for determining limit cyc les of strongly non-linear oscillators of the form x + g(x) = mu f(x, x), where g(x) is an arbitrary non-linear function of the displacement x, and mu has a small to moderate value. By assuming that x = a cos p hi + b and d phi/dt = Phi(phi), where Phi(phi) is 2 pi-periodic in phi , the method allows a, b and Phi(phi) to be calculated to any desired degree of accuracy by the iterative method, and the limit cycle phase portraits are in very good agreement with the corresponding numerical solutions of the differential equations.