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Zbl 1138.70006
Albouy, Alain; Fu, Yanning; Sun, Shanzhong
Symmetry of planar four-body convex central configurations. (English)
[J] Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 464, No. 2093, 1355-1365 (2008). ISSN 1364-5021; ISSN 1471-2946/e

Summary: We study the relationship between the masses and 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 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.

MSC 2000:: *70F10 n-body problem

Keywords: equal masses

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Zentralblatt MATH Berlin [Germany]