Classification of four-body central configurations with three equal masses

DOI10.1016/j.jmaa.2009.09.040zbMath1301.70008OpenAlexW2063338513MaRDI QIDQ1046503

Zhifu Xie, Junping Shi

Publication date: 22 December 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://scholarworks.wm.edu/cgi/viewcontent.cgi?article=2256&context=aspubs

zbMATH Keywords

bifurcationcentral configurationimplicit function theorem\(N\)-body problemconvex and concave central configuration

Mathematics Subject Classification ID

Celestial mechanics (70F15) (n)-body problems (70F10)

Related Items (15)

Number of central configurations and singular surfaces in the mass space in the collinear four-body problem ⋮ Central configurations for Newtonian \(N+2p+1\)-body problems ⋮ On the uniqueness of convex central configurations in the planar 4-body problem ⋮ Central configurations of four bodies with gravitational charges of both signs ⋮ Inverse problem of central configurations and singular curve in the collinear 4-body problem ⋮ Twisted stacked central configurations for the spatial nine-body problem ⋮ A continuum of periodic solutions to the planar four-body problem with two pairs of equal masses ⋮ Central configurations of four bodies with an axis of symmetry ⋮ Stacked central configurations for Newtonian \({N+2p}\)-body problems ⋮ Planar \(N\)-body central configurations with a homogeneous potential ⋮ The golden ratio and super central configurations of the \(n\)-body problem ⋮ Planar symmetric concave central configurations in Newtonian four-body problems ⋮ Rational parameterizations approach for solving equations in some dynamical systems problems ⋮ Super central configurations of the n-body problem ⋮ Central configurations for \((pN+gN)\)-body problems

Cites Work

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• Inverse problem of central configurations and singular curve in the collinear 4-body problem
• Collinear central configuration in four-body problem
• Finiteness of relative equilibria of the four-body problem
• The central configurations of four masses \(x, - x, y, - y\)
• Regularization of simultaneous binary collisions and solutions with singularity in the collinear four-body problem
• Measure of degenerate relative equilibria. I
• Finiteness and bifurcations of some symmetrical classes of central configurations
• Four-body central configurations with some equal masses
• On central configurations
• Convex central configurations for the \(n\)-body problem
• On the central configurations of the planar restricted four-body problem
• Topology and mechanics. II: The planar \(n\)-body problem
• Convex four-body central configurations with some equal masses
• Symmetry of planar four-body convex central configurations
• Collinear central configurations in the n-body problem with general homogeneous potential
• Bifurcations of relative equilibria in the 4- and 5-body problem
• Admissible Shapes of 4-Body Non-collinear Relative Equilibria

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