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Transport in dynamical astronomy and multibody problems

Dellnitz, Michael and Junge, Oliver and Koon, Wang Sang and Lekien, Francois and Lo, Martin W. and Marsden, Jerrold E. and Padberg, Kathrin and Preis, Robert and Ross, Shane D. and Thiere, Bianca (2005) Transport in dynamical astronomy and multibody problems. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 15 (3). pp. 699-727. ISSN 0218-1274. doi:10.1142/S0218127405012545.

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We combine the techniques of almost invariant sets (using tree structured box elimination and graph partitioning algorithms) with invariant manifold and lobe dynamics techniques. The result is a new computational technique for computing key dynamical features, including almost invariant sets, resonance regions as well as transport rates and bottlenecks between regions in dynamical systems. This methodology can be applied to a variety of multibody problems, including those in molecular modeling, chemical reaction rates and dynamical astronomy. In this paper we focus on problems in dynamical astronomy to illustrate the power of the combination of these different numerical tools and their applicability. In particular, we compute transport rates between two resonance regions for the three-body system consisting of the Sun, Jupiter and a third body (such as an asteroid). These resonance regions are appropriate for certain comets and asteroids.

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Additional Information:©2005 World Scientific Publishing Company. Received April 28, 2004; revised July 5, 2004. This research was partly supported by the DAAD, DFG Priority Program 1095, NSF-ITR grant ACI- 0204932, a Max Planck Research Award and the California Institute of Technology President’s Fund. This work was carried out in part at the Jet Propulsion Laboratory and California Institute of Technology under a contract with National Aeronautics and Space Administration.
Funding AgencyGrant Number
DFG Priority Program 1095UNSPECIFIED
NSF-ITRACI- 0204932
Max Planck Research AwardUNSPECIFIED
Caltech President’s FundUNSPECIFIED
Subject Keywords:Three-body problem; transport rates; dynamical systems; almost invariant sets; graph partitioning; set-oriented methods; invariant manifolds; lobe dynamics
Issue or Number:3
Record Number:CaltechAUTHORS:DELijbc05
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4875
Deposited By: Lindsay Cleary
Deposited On:12 Sep 2006
Last Modified:08 Nov 2021 20:20

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