Journal Article

Shadowing unstable orbits of the Sitnikov elliptic three-body problem

D. J. Urminsky

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 407, issue 2, pages 804-811
Published in print September 2010 | ISSN: 0035-8711
Published online September 2010 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2010.16974.x
Shadowing unstable orbits of the Sitnikov elliptic three-body problem

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Errors in numerical simulations of gravitating systems can be magnified exponentially over short periods of time. Numerical shadowing provides a way of demonstrating that the dynamics represented by numerical simulations are representative of true dynamics. Using the Sitnikov problem as an example, it is demonstrated that unstable orbits of the three-body problem can be shadowed for long periods of time. In addition, it is shown that the stretching of phase space near escape and capture regions is a cause for the failure of the shadowing refinement procedure.

Keywords: methods: numerical; celestial mechanics

Journal Article.  5416 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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