Geometric mechanics and the dynamics of asteroid pairs

Shane D. Ross
Control and Dynamical Systems, California Institute of Technology
MC 107-81, Pasadena, CA 91125, USA. E-mail:

(with Wang Sang Koon, Jerrold E. Marsden, Martin W. Lo, and Daniel J. Scheeres)


The purpose of this paper is to give some preliminary results as well to describe the general setting for the application of techniques from geometric mechanics and dynamical systems transport calculations to the problem of asteroid pairs and to the calculation of 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 FBP's 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 dynamics of asteroid pairs using techniques that are generally applicable to many other FBP's. 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 determinging 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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