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

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

2011-11-18

arxiv.org/abs/1111.4245v1

Astronomy and Astrophysics

Astrophysics

Earth and Planetary Astrophysics

Preprint

Scientific paper

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=4 bodies.

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