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Explicit Adaptive Symplectic (Easy) Integrators: A Scaling Invariant Generalisation of the Levi-Civitaand KS Regularisations

Authors :
Sergio Blanes
Chris Budd
Source :
Celestial Mechanics and Dynamical Astronomy. 89:383-405
Publication Year :
2004
Publisher :
Springer Science and Business Media LLC, 2004.

Abstract

We present a generalisation of the Levi-Civita and Kustaanheimo-Stiefel regularisation. This allows the use of more general time rescalings. In particular, it is possible to find a regularisation which removes the singularity of the equations and preserves scaling invariance. In addition, these equations can, in certain cases, be integrated with explicit symplectic Runge-Kutta-Nystrom methods. The combination of both techniques gives an explicit adaptive symplectic (EASY) integrator. We apply those methods to some perturbations of the Kepler problem and illustrate, by means of some numerical examples, when scaling invariant regularisations are more efficient that the LC/KS regularisation.

Details

ISSN :
09232958
Volume :
89
Database :
OpenAIRE
Journal :
Celestial Mechanics and Dynamical Astronomy
Accession number :
edsair.doi...........fe53f603479bf2587a1b0d407fbe340c