Geometric numerical integration applied to the elastic pendulum at higher order resonance

Abstract

In this paper we study the performance of a symplectic numerical integrator based on the splitting method This method is applied to a subtle problem ie higher order resonance of the elastic pendulum In order to numerically study the phase space of the elastic pendulum at higher order resonance a numerical integrator which preserves qualitative features after long integration times is needed We show by means of an example that our symplectic method oers a relatively cheap and accurate numerical integrator