New classes of spatial central configurations for \(N + N + 2\)-body problem
type: Item
instance of: scholarly article
title: New classes of spatial central configurations for \(N + N + 2\)-body problem
zbMATH Open document ID: 1242.70021
DOI: 10.1155/2012/948356
author: Xuefei Liu
author: Chuntao Zhang
author: Jianmei Luo
author: Gan Zhang
published in: Abstract and Applied Analysis
publication date: 2012-07-18T00:00:00Z
review text: Summary: Under arbitrary masses, we discuss the existence of new families of spatial central configurations for the \(N + N + 2\)-body problem, \(N \geq 2\). 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 \(\Gamma_1 \cup \Gamma_2\), and the other two bodies are symmetrically located on the straight line that is perpendicular to the plane that contains \(\Gamma_1 \cup \Gamma_2\) and passes through the geometric center of \(\Gamma_1 \cup \Gamma_2\). 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.
Mathematics Subject Classification ID: 70F10
zbMATH DE Number: 6058181
Wikidata QID: Q58697138
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/948356
OpenAlex ID: W1529650279
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description: scientific article; zbMATH DE number 6058181