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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:20111207-105304153

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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 L_1 and the other around L_2, 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 L_1 and L_2 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
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.166509 DOIUNSPECIFIED
http://chaos.aip.org/resource/1/chaoeh/v10/i2/p427_s1PublisherUNSPECIFIED
http://hdl.handle.net/2014/17457OtherUNSPECIFIED
Additional Information:© 2000 American Institute of Physics. Received 21 May 1999; accepted for publication 6 December 1999. We thank Gerard Gómez 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 Martínez, Richard McGehee, William McLaughlin, J. M. Petit, Linda Petzold, Nicole Rappaport, Carles Simó, 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.
Funders:
Funding AgencyGrant Number
Caltech President’s FundUNSPECIFIED
NASA Advanced Concepts Research ProgramUNSPECIFIED
Genesis ProjectUNSPECIFIED
NSFKDI/ATM-9873133
Subject Keywords:comets, asteroids, solar system, celestial mechanics, N-body problems, nonlinear dynamical systems, chaos, numerical analysis
Other Numbering System:
Other Numbering System NameOther Numbering System ID
JPL Technical Reports99-0910
Classification Code:PACS: 95.10.Ce; 45.50.Pk; 05.45.Pq; 96.30.Cw; 96.30.Ys; 45.50.Jf; 02.60.-x
Record Number:CaltechAUTHORS:20111207-105304153
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20111207-105304153
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:28344
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:14 May 2012 22:54
Last Modified:26 Dec 2012 14:34

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