New classes of spatial central configurations for \(N + N + 2\)-body problem
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.
scientific article; zbMATH DE number 6058181
scientific article