Central configurations of nested regular polyhedra for the spatial \(2n\)-body problem

DOI10.1016/j.geomphys.2008.05.003zbMath1146.70007OpenAlexW2127931772MaRDI QIDQ950275

Montserrat Corbera, Jaume Llibre

Publication date: 22 October 2008

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2008.05.003

Mathematics Subject Classification ID

(n)-body problems (70F10)

Related Items (23)

Topological bifurcations of spatial central configurations in the \(N\)-body problem ⋮ Convex but not strictly convex central configurations ⋮ Stacked central configurations for the spatial six-body problem ⋮ Double-antiprism central configurations of the \(3n\)-body problem ⋮ Stacked central configurations for the spatial seven-body problem ⋮ New classes of spatial central configurations for the \(n+3\)-body problem ⋮ Two classes of stacked central configurations for the spatial \(2n+1\)-body problem: nested regular polyhedra plus one ⋮ A Theory of Central Measures for Celestial Mechanics ⋮ On the central configurations of the n-body problem ⋮ New classes of spatial central configurations for \(N + N + 2\)-body problem ⋮ On the existence of central configurations of \(p\) nested regular polyhedra ⋮ Inverse problem of central configurations and singular curve in the collinear 4-body problem ⋮ Stacked central configurations in the 5-vortex problem ⋮ New spatial central configurations in the 5-body problem ⋮ Central configurations of the collinear three-body problem and singular surfaces in the mass space ⋮ The golden ratio and super central configurations of the \(n\)-body problem ⋮ Collinear central configurations in the n-body problem with general homogeneous potential ⋮ New classes of spatial central configurations for the 7-body problem ⋮ Homothetic radial solutions of the Newtonian general spatial \((N+1)\)-body problem ⋮ Central configurations of nested rotated regular tetrahedra ⋮ Central configurations of three nested regular polyhedra for the spatial \(3n\)-body problem ⋮ Super central configurations of the n-body problem ⋮ Spatial bi-stacked central configurations formed by two dual regular polyhedra

Cites Work

• The existence and uniqueness of central configurations for nested regular octahedron
• On the manifolds of total collapse orbits and of completely parabolic orbits for the n-body problem
• Symmetric central configurations of the spatial n-body problem
• Total collison, completely parabolic motions and homothety reduction in the \(n\)-body problem
• Topology and mechanics. II: The planar \(n\)-body problem
• Central configurations of nested regular tetrahedrons
• Periodic solutions for planar 2N-body problems
• Nested regular polygon solutions of \(2N\)-body problem

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