Stability and integrability in the planar general three-body problem

Details Stability and integrability in the planar general three-body problem Stability and integrability in the planar general three-body problem

Jul 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983aj.....88.1064h&link_type=abstract

Astronomical Journal (ISSN 0004-6256), vol. 88, July 1983, p. 1064-1073. Research supported by the Natural Sciences and Engineer

Statistics

2

Celestial Mechanics, Entropy (Statistics), Kepler Laws, Orbit Perturbation, Orbital Elements, Systems Stability, Three Body Problem, Binary Stars, Eccentric Orbits, Hierarchies, Hill Method, Kolmogoroff Theory, Liapunov Functions, Mass Ratios, Numerical Integration

Scientific paper

The Kolmogorov entropy is applied to discuss the stability and integrability of the planar general three-body problem with equal masses. Our numerical experiments show that the entropy is a useful and sensitive tool to investigate the stability problem. Stability boundaries for initial semimajor axis are given for different values of initial eccentricities, and are compared with those in Hill stability. In particular, the evolution of the elements and the difference between direct and retrograde orbits are explored. The integrability of this system is also discussed. We argue that there exist local additional integrals when the initial elements are situated inside the stable region, or far outside the stability boundary. The reliability of the check of numerical accuracy by use of the energy integral is examined. We find that this check is unreliable when the initial elements are close to the stability boundary.

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