Koon, W. S., J. E. Marsden, S. Ross, M. Lo, and D. J. Scheeres
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.