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2012 New Classes of Spatial Central Configurations for N + N + 2-Body Problem
Liu Xuefei, Zhang Chuntao, Luo Jianmei, Zhang Gan
Abstr. Appl. Anal. 2012: 1-19 (2012). DOI: 10.1155/2012/948356


Under arbitrary masses, in this paper, we discuss the existence of new families of spatial central configurations for the N + N + 2-body problem, N 2 . We study some necessary conditions and sufficient conditions for a families of spatial double pyramidical central configurations (d.p.c.c.), where 2N bodies are at the vertices of a nested regular N-gons Γ 1 Γ 2 , and the other two bodies are symmetrically located on the straight line that is perpendicular to the plane that contains Γ 1 Γ 2 and passes through the geometric center of Γ 1 Γ 2 . We prove that if the bodies are in a d.p.c.c., then the masses on each N-gon are equal, and the other two are also equal. And also we prove the existence and uniqueness of the central configurations for any given ratios of masses.


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Liu Xuefei. Zhang Chuntao. Luo Jianmei. Zhang Gan. "New Classes of Spatial Central Configurations for N + N + 2-Body Problem." Abstr. Appl. Anal. 2012 1 - 19, 2012.


Published: 2012
First available in Project Euclid: 14 December 2012

zbMATH: 1242.70021
MathSciNet: MR2922912
Digital Object Identifier: 10.1155/2012/948356

Rights: Copyright © 2012 Hindawi


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