1111.4245 (D. J. Scheeres)

Minimum Energy Configurations in the $N$-Body Problem and the Celestial
Mechanics of Granular Systems    [PDF]

D. J. Scheeres

Minimum energy configurations in celestial mechanics are investigated. It is shown that this is not a well defined problem for point-mass celestial mechanics but well-posed for finite density distributions. This naturally leads to a granular mechanics extension of usual celestial mechanics questions such as relative equilibria and stability. This paper specifically studies and finds all relative equilibria and minimum energy configurations for $N=1,2,3$ and develops hypotheses on the relative equilibria and minimum energy configurations for $N\gg 1$ bodies.

View original: http://arxiv.org/abs/1111.4245