Central configurations with many small masses

DOI10.1016/0022-0396(91)90137-XzbMath0724.70015MaRDI QIDQ758239

Zhihong Xia

Publication date: 1991

Published in: Journal of Differential Equations (Search for Journal in Brave)

zbMATH Keywords

Hausdorff measurecentral configurationsmethod of analytical continuation

Mathematics Subject Classification ID

Computational methods for problems pertaining to mechanics of particles and systems (70-08) (n)-body problems (70F10) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)

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Finiteness of relative equilibria of the four-body problem ⋮ The reduction of the linear stability of elliptic Euler-Moulton solutions of the \(n\)-body problem to those of 3-body problems ⋮ Convex central configurations for the \(n\)-body problem ⋮ Central configurations of the 4-body problem with masses \(m_1 = m_2 > m_3 = m_4 = m > 0\) and \(m\) small ⋮ Convex four-body central configurations with some equal masses ⋮ A stochastic optimization algorithm for analyzing planar central and balanced configurations in the \(n\)-body problem ⋮ Central configurations on the plane with \(N\) heavy and \(k\) light bodies ⋮ Relative equilibria with clusters of small masses ⋮ Existence and Stability of Four-Vortex Collinear Relative Equilibria with Three Equal Vorticities ⋮ Central configurations for Newtonian \(N+2p+1\)-body problems ⋮ The symmetric central configurations of the 4-body problem with masses \(m_1 = m_2 \neq m_3 = m_4\) ⋮ Reduced spaces and their relation to relative equilibria ⋮ Finiteness of relative equilibria in the planar generalized \(N\)-body problem with fixed subconfigurations ⋮ Linear stability of elliptic relative equilibria of four-body problem with two infinitesimal masses ⋮ Toward finiteness of central configurations for the planar six-body problem by symbolic computations. I: Determine diagrams and orders ⋮ On the central configurations of the n-body problem ⋮ Bifurcations and enumeration of central configurations of some planar restricted problems ⋮ A limit of nonplanar 5-body central configurations is nonplanar ⋮ Open problem 1: Are Palmore's ``ignored estimates on the number of planar central configurations correct? ⋮ On the existence of central configurations of \(p\) nested regular polyhedra ⋮ Finiteness of central configurations of five bodies in the plane ⋮ Singular continuation of planar central configurations with clusters of bodies ⋮ Tangential trapezoid central configurations ⋮ Fixed point indices of central configurations ⋮ Fixed points and the inverse problem for central configurations ⋮ New central configurations of the \((n + 1)\)-body problem ⋮ Stacked central configurations for Newtonian \({N+2p}\)-body problems ⋮ Planar \(N\)-body central configurations with a homogeneous potential ⋮ Periodic orbits in the four body problem with large and small masses ⋮ Hjelmslev quadrilateral central configurations ⋮ Bifurcations of Central Configurations in the Four-Body Problem with Some Equal Masses ⋮ Bicentric quadrilateral central configurations ⋮ Planar central configuration estimates in the n-body problem ⋮ Applying the symmetry groups to study the \(n\) body problem ⋮ On central configurations ⋮ Central configurations of the five-body problem with equal masses ⋮ On centered co-circular central configurations of the \(n\)-body problem ⋮ Bifurcation of Relative Equilibria of the (1+3)-Body Problem ⋮ A note on the Dziobek central configurations ⋮ Equilateral chains and cyclic central configurations of the planar five-body problem ⋮ The co-circular central configurations of the 5-body problem ⋮ On the relative equilibria of the (rhombus+1)-body problem ⋮ Central configurations for \((pN+gN)\)-body problems

Cites Work

• The manifold structure for collision and for hyperbolic-parabolic orbits in the n-body problem
• Some topology of n-body problems
• Measure of degenerate relative equilibria. I
• Topology and mechanics. I
• Relative equilibria of the four-body problem
• Bifurcations of Relative Equilibria in the N-Body and Kirchhoff Problems
• On the role and the properties ofn body central configurations
• Central configurations of four bodies with one inferior mass
• Collinear relative equilibria of the planarN-body problem
• Classifying relative equilibria. I

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