Geometric Numerical Integration Applied to The Elastic Pendulum at Higher Order Resonance

Details Geometric Numerical Integration Applied to The Elastic Pendulum at Higher Order Resonance Geometric Numerical Integration Applied to The Elastic Pendulum at Higher Order Resonance

2000-08-25

arxiv.org/abs/nlin/0008033v1

Nonlinear Sciences

Chaotic Dynamics

15 pages, 6 figures

Scientific paper

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.

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