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Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics

Koon, Wang Sang and Lo, Martin W. and Marsden, Jerrold E. and Ross, Shane D. (2000) Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics. Chaos, 10 (2). pp. 427-469. ISSN 1054-1500. http://resolver.caltech.edu/CaltechAUTHORS:KOOcha00

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Abstract

In this paper we apply dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted three-body problem. These related phenomena have been of concern for some time in topics such as the capture of comets and asteroids and with the design of trajectories for space missions such as the Genesis Discovery Mission. The main new technical result in this paper is the numerical demonstration of the existence of a heteroclinic connection between pairs of periodic orbits: one around the libration point L1 and the other around L2, with the two periodic orbits having the same energy. This result is applied to the resonance transition problem and to the explicit numerical construction of interesting orbits with prescribed itineraries. The point of view developed in this paper is that the invariant manifold structures associated to L1 and L2 as well as the aforementioned heteroclinic connection are fundamental tools that can aid in understanding dynamical channels throughout the solar system as well as transport between the "interior" and "exterior" Hill's regions and other resonant phenomena.


Item Type:Article
Additional Information:© 2000 American Institute of Physics. Received 21 May 1999; accepted for publication 6 December 1999. We thank Gerard Gomez and Josep Masdemont for many helpful discussions and for sharing their wonderful software tools with us. We thank Donald Yeomans and Alan Chamberlin for the JPL Horizons integrator which generated the comet orbits. We thank Edward Belbruno and Brian Marsden for an advanced copy of their comet paper. We also wish to thank the following colleagues for helpful discussions and comments: Brian Barden, Julia Bell, Peter Goldreich, Kathleen Howell, Angel Jorba, Andrew Lange, Jaume Llibre, Regina Martinez, Richard McGehee, William McLaughlin, J. M. Petit, Linda Petzold, Nicole Rappaport, Carles Simo, Scott Tremaine, Stephen Wiggins, and Roby Wilson. This work was carried out at the Jet Propulsion Laboratory and the California Institute of Technology under a contract with the National Aeronautics and Space Administration. In addition, the work was partially supported by the Caltech President’s fund, the NASA Advanced Concepts Research Program, The Genesis Project, and National Science Foundation Grant No. KDI/ATM-9873133.
Subject Keywords:comets; asteroids; solar system; celestial mechanics; N-body problems; nonlinear dynamical systems; chaos; numerical analysis
Record Number:CaltechAUTHORS:KOOcha00
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:KOOcha00
Alternative URL:http://dx.doi.org/10.1063/1.166509
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4385
Collection:CaltechAUTHORS
Deposited By: Lindsay Cleary
Deposited On:21 Aug 2006
Last Modified:26 Dec 2012 08:59

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