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
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.