Symmetry of Planar Four-Body Convex Central Configurations

Details Symmetry of Planar Four-Body Convex Central Configurations Symmetry of Planar Four-Body Convex Central Configurations

2007-06-08

arxiv.org/abs/0706.1194v1

Physics

Mathematical Physics

12 pages

Scientific paper

10.1098/rspa.2007.0320

We study the relationship between the masses and the geometric properties of central configurations. We prove that in the planar four-body problem, a convex central configuration is symmetric with respect to one diagonal if and only if the masses of the two particles on the other diagonal are equal. If these two masses are unequal, then the less massive one is closer to the former diagonal. Finally, we extend these results to the case of non-planar central configurations of five particles.

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