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Published March 2005 | public
Journal Article

Transport in dynamical astronomy and multibody problems

Abstract

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.

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.

Additional details

Created:
August 22, 2023
Modified:
October 16, 2023