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Hill Stability of Configurations in the Full N-Body Problem

Published online by Cambridge University Press:  01 March 2016

D. J. Scheeres
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Abstract

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Rigorous results on Hill Stability for the classical N-body problem are in general unknown for N ≥ 3, due to the complex interactions that may occur between bodies and the many different outcomes which may occur. However, the addition of finite density for the bodies along with a rigidity assumption on their mass distribution allows for Hill stability to be easily established. In this note we generalize results on Hill stability developed for the Full 3-body problem and show that it can be applied to the Full N-body problem. Further, we find that Hill Stability concepts can be applied to identify types of configurations which can escape and types which cannot as a function of the system energy.

Type
Contributed Papers
Information
Proceedings of the International Astronomical Union , Volume 10 , Issue S318: Asteroids: New Observations, New Models , August 2015 , pp. 128 - 134
Copyright
Copyright © International Astronomical Union 2016 

References

Scheeres, D. J.. Minimum energy configurations in the n-body problem and the celestial mechanics of granular systems. Celestial Mechanics and Dynamical Astronomy, 113 (3):291–320, 2012.Google Scholar
Scheeres, DJ. Hill stability in the full 3-body problem. Proceedings of the International Astronomical Union, 9 (S310):134–137, 2014.CrossRefGoogle Scholar
Scheeres, DJ. Relative equilibria in the full n-body problem with applications to the equal mass problem. Mathematics for Industry: Celestial and Space Mechanics, Bonnard and Chyba (Eds), 2016. ISBN 978-3-319-27462-1.Google Scholar
Smale, S.. Topology and mechanics. i. Inventiones mathematicae, 10 (4):305–331, 1970.CrossRefGoogle Scholar