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

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 i.e. 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 offers a relatively cheap and accurate numerical integrator.