Mathematics – Dynamical Systems
Scientific paper
May 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989aj.....97.1496m&link_type=abstract
Astronomical Journal (ISSN 0004-6256), vol. 97, May 1989, p. 1496-1509.
Mathematics
Dynamical Systems
22
Orbital Mechanics, Three Body Problem, Equations Of Motion, Error Analysis
Scientific paper
This work is a quantitative analysis of the advantages of the Bulirsch-Stoer (1966) method, demonstrating that this method is certainly worth considering when working with small N dynamical systems. The results, qualitatively suspected by many users, are quantitatively confirmed as follows: (1) the Bulirsch-Stoer extrapolation method is very fast and moderately accurate; (2) regularization of the equations of motion stabilizes the error behavior of the method and is, of course, essential during close approaches; and (3) when applicable, a manifold-correction algorithm reduces numerical errors to the limits of machine accuracy. In addition, for the specific case of the restricted three-body problem, even a small eccentricity for the orbit of the primaries drastically affects the accuracy of integrations, whether regularized or not; the circular restricted problem integrates much more accurately.
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