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

Authors:
J. M. Tuwankotta;G. R. W. Quispel
Affiliations:
Mathematisch Instituut, Universiteit Utrecht, P.O. Box 80.010, 3508 TA Utrecht, The Netherlands;School of Mathematical and Statistical Sciences, La Trobe University, Bundoora, Vic. 3083, Australia
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

Citing 2
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A nodal position finite element method for plane elastic problems

Finite Elements in Analysis and Design

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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 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.