Under arbitrary masses, in this paper, we discuss the existence of new families of spatial central configurations for the N + N + 2-body problem, . 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 , and the other two bodies are symmetrically located on the straight line that is perpendicular to the plane that contains and passes through the geometric center of . 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.
"New Classes of Spatial Central Configurations for N + N + 2-Body Problem." Abstr. Appl. Anal. 2012 1 - 19, 2012. https://doi.org/10.1155/2012/948356