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Zbl 1112.70010
Zhu, Changrong
Central configurations of nested regular tetrahedrons. (English)
[J] J. Math. Anal. Appl. 312, No. 1, 83-92 (2005). ISSN 0022-247X

Summary: We study the necessary and sufficient conditions about nested regular tetrahedrons, and prove that some nests do not form central configurations, some can. The necessary and sufficient conditions of central configurations are the masses of the inner layer and outer layer must equal, respectively, and the ratios of masses and distances of inner and outer layer must satisfy an equation.
MSC 2000:
*70F10 n-body problem

Keywords: Central configurations; Nested regular tetrahedrons; Celestial mechanics

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