New Classes of Spatial Central Configurations for N + N + 2-Body Problem

Liu Xuefei, Zhang Chuntao, Luo Jianmei and Zhang Gan

Abstract and Applied Analysis, 2012, vol. 2012, 1-19

Abstract:

Under arbitrary masses, in this paper, we discuss the existence of new families of spatial central configurations for the N + N + 2-body problem, ð ‘ â‰¥ 2 . We study some necessary conditions and sufficient conditions for a families of spatial double pyramidical central configurations (d.p.c.c.), where 2 N 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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:948356

DOI: 10.1155/2012/948356

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