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Geometric Mechanics and the Dynamics of Asteroid Pairs

Koon, Wang Sang and Marsden, Jerrold E. and Ross, Shane and Lo, Martin and Scheeres, Dan J. (2004) Geometric Mechanics and the Dynamics of Asteroid Pairs. In: Astrodynamics, space missions, and chaos. Annals of the New York Academy of Sciences. No.1017. New York Academy of Sciences , New York, pp. 11-38. ISBN 9781573315135.

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The purpose of this paper is to describe the general setting for the application of techniques from geometric mechanics and dynamical systems to the problem of asteroid pairs. It also gives some preliminary results on transport calculations and the associated problem of calculating binary asteroid escape rates. The dynamics of an asteroid pair, consisting of two irregularly shaped asteroids interacting through their gravitational potential is an example of a full body problem or FBP in which two or more extended bodies interact. One of the interesting features of the binary asteroid problem is that there is coupling between their translational and rotational degrees of freedom. General FBPs have a wide range of other interesting aspects as well, including the 6-DOF guidance, control, and dynamics of vehicles, the dynamics of interacting or ionizing molecules, the evolution of small body, planetary, or stellar systems, and almost any other problem where distributed bodies interact with each other or with an external field. This paper focuses on the specific case of asteroid pairs using techniques that are generally applicable to many other FBPs. This particular full 2-body problem (F2BP) concerns the dynamical evolution of two rigid bodies mutually interacting via a gravitational field. Motivation comes from planetary science, where these interactions play a key role in the evolution of asteroid rotation states and binary asteroid systems. The techniques that are applied to this problem fall into two main categories. The first is the use of geometric mechanics to obtain a description of the reduced phase space, which opens the door to a number of powerful techniques such as the energy-momentum method for determining the stability of equilibria and the use of variational integrators for greater accuracy in simulation. Secondly, techniques from computational dynamical systems are used to determine phase space structures important for transport phenomena and dynamical evolution.

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Additional Information:© 2004 New York Academy of Sciences. Article first published online: 12 JAN 2006. This research was partially supported by a Max Planck Research Award and NSF ITR grant ACI-0204932. The work described in this paper was carried out in part at the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA.
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Max Planck Research AwardUNSPECIFIED
Subject Keywords:geometric mechanics; dynamics; asteroid pairs; full-body problem
Series Name:Annals of the New York Academy of Sciences
Issue or Number:1017
Record Number:CaltechAUTHORS:20101015-093844631
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Official Citation:Koon, W.-S., J. E. Marsden, et al. (2004). "Geometric Mechanics and the Dynamics of Asteroid Pairs." Annals of the New York Academy of Sciences 1017(1): 11-38.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20434
Deposited By: Ruth Sustaita
Deposited On:30 Nov 2010 22:05
Last Modified:08 Nov 2021 23:59

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