The elliptic core of nonlinear oscillators

Abstract We devise a method which is apt for the approximation of periodic solutions of strongly nonlinear or statically unstable oscillating systems. To this purpose we consider firstly a system which is canonically associated with ours, the so called elliptic core, and solve it in closed form; this solution is then used as a basis for the construction of a suitable set of trial functions which enable us to apply the Galerkin method in order to obtain the sought approximation. The technique is employed in a number of vibrating systems previously considered in the literature; the results are supported by numerical evidence. Finally we present some further results concerning the relationship between amplitude and period of nonlinear oscillators.