Computer Science – Performance
Scientific paper
Sep 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998dda....30.0603r&link_type=abstract
American Astronomical Society, DDA meeting #30, #06.03; Bulletin of the American Astronomical Society, Vol. 30, p.1143
Computer Science
Performance
Scientific paper
We examine the dynamical stability of the Wisdom-Holman symplectic mapping (Wisdom & Holman 1991; cf. Kinoshita, Yoshida, & Nakai 1991) and the symplectic potential-splitting method (Lee, Duncan, & Levison 1997; cf. Skeel & Biesiadecki 1994) applied to the integration of eccentric orbits in nearly-Keplerian systems, focusing primarily on the perturbed two body problem. In particular, we use the Stark problem and the two fixed point problem to determine the relative performance of several variations of the aforementioned algorithms. The former incorporates eccentric motion without close encounters; the latter allows them to be included in a controlled manner. Both test problems have the advantages of complete regularity, easily classified orbital types, and practical analytic solution in terms of elliptic functions and integrals. The performance of algorithms based on Stark motion instead of Kepler motion (similar to, though independent of, those of Newman et al. 1997) is also investigated. We find that regularization of the Wisdom-Holman mapping, proposed by Mikkola (1997), produces a highly efficient and robust method for integrating eccentric orbits not subject to close encounters. With close encounters, a modified form of the potential-splitting method is found to perform very well. Because of their relative inefficiency, and the rather weak similarity between motion in the Stark potential and that in real N-body systems, Stark-based methods are found to be uncompetitive with the other methods considered.
Holman Matthew
Rauch Kevin P.
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