Planar \(N\)-body central configurations with a homogeneous potential
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Publication:2005616
DOI10.1007/s10569-019-9898-0zbMath1451.70023arXiv1810.13011OpenAlexW2944206193WikidataQ64298303 ScholiaQ64298303MaRDI QIDQ2005616
Publication date: 8 October 2020
Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1810.13011
(n)-body problems (70F10) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)
Related Items
Spatial equilateral chain central configurations of the five-body problem with a homogeneous potential ⋮ A stochastic optimization algorithm for analyzing planar central and balanced configurations in the \(n\)-body problem ⋮ Stacked Central Configurations with a Homogeneous Potential in \(\mathbb{R}^3\)
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Cites Work
- Stability of Relative Equilibria in the Problem of N+1 Vortices
- Solving polynomial systems globally invariant under an action of the symmetric group and application to the equilibria of N vortices in the plane
- Bifurcations and Enumeration of Classes of Relative Equilibria in the Planar Restricted Four-Body Problem
- Stacked central configurations: new examples in the planar five-body problem
- Permanent Configurations in the Problem of Five Bodies
- Permanent Configurations in the n-Body Problem
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Splendid isolation: local uniqueness of the centered co-circular relative equilibria in the \(N\)-body problem
- Finiteness of spatial central configurations in the five-body problem
- New stacked central configurations for the planar 5-body problem
- The symmetric central configurations of the 4-body problem with masses \(m_1 = m_2 \neq m_3 = m_4\)
- Relative equilibria in the four-vortex problem with two pairs of equal vorticities
- Relative equilibria of the \((1+N)\)-vortex problem
- Twisted angles for central configurations formed by two twisted regular polygons
- Finiteness of central configurations of five bodies in the plane
- Four-body central configurations with adjacent equal masses
- Central configurations and mutual differences
- Central configurations of four bodies with an axis of symmetry
- Symmetric planar central configurations of five bodies: Euler plus two
- Central configurations for the planar Newtonian four-body problem
- Symmetry of the restricted \(4+1\) body problem with equal masses
- Euler configurations and quasi-polynomial systems
- Existence of symmetric central configurations
- Central configurations with many small masses
- On the number of central configurations in the n-body problem
- Linear stability of the Lagrangian triangle solutions for quasihomogeneous potentials
- Finiteness of relative equilibria of the four-body problem
- Finiteness of relative equilibria in the planar generalized \(N\)-body problem with fixed subconfigurations
- Open problem 1: Are Palmore's ``ignored estimates on the number of planar central configurations correct?
- Chaotic dynamics near triple collision
- Morse theory and central configurations in the spatial \(N\)-body problem
- Triple and quadruple nested central configurations for the planar \(n\)-body problem
- Rosette central configurations, degenerate central configurations and bifurcations
- Central configurations of the five-body problem with equal masses
- Stability of relative equilibria and Morse index of central configurations
- Classification of four-body central configurations with three equal masses
- Central configurations of the N-body problem via equivariant Morse theory
- Origin and infinity manifolds for mechanical systems with homogeneous potentials
- Triple collision in the planar isosceles three body problem
- The \(N\)-gon is not a local minimum of \(U^ 2 I\) for \(N \geq{} 7\)
- Linear stability of a self-gravitating ring
- The collinear central configuration of \(n\) equal masses
- Triple collision in the collinear three-body problem
- Some topology of n-body problems
- Integral manifolds of the \(N\)-body problem
- Linear stability of relative equilibria with a dominant mass
- Relative equilibria with clusters of small masses
- The \(n\)-body problem and mutual distances
- Finiteness and bifurcations of some symmetrical classes of central configurations
- On a paper of Moeckel on central configurations
- Mathematical problems for the next century
- Four-body central configurations with some equal masses
- Linear stability of the elliptic Lagrangian triangle solutions in the three-body problem
- A four-body convex central configuration with perpendicular diagonals is necessarily a kite
- A family of stacked central configurations in the planar five-body problem
- Central configurations and a theorem of Palmore
- Four-body central configurations with one pair of opposite sides parallel
- Bifurcation of central configuration in the \(2N+1\) body problem
- Central configurations of the planar coorbital satellite problem
- A continuum of relative equilibria in the five-body problem
- On central configurations
- Morse theory indomitable
- Continua of central configurations with a negative mass in the \(n\)-body problem
- On the existence of central configurations of \(p\) nested \(n\)-gons
- Finiteness of kite relative equilibria in the five-vortex and five-body problems
- Linear instability of relative equilibria for \(n\)-body problems in the plane
- Central configurations for \((pN+gN)\)-body problems
- Convex central configurations of the 4-body problem with two pairs of equal adjacent masses
- New central configurations for the planar 5-body problem
- On the central configurations of the planar restricted four-body problem
- Nested regular polygon solutions for planar \(2N\)-body problems
- Topology and mechanics. I
- Topology and mechanics. II: The planar \(n\)-body problem
- On the integral manifolds of the n-body problem
- Convex four-body central configurations with some equal masses
- LINEAR STABILITY IN THE 1 + N-GON RELATIVE EQUILIBRIUM
- Generic Finiteness for Dziobek Configurations
- Bifurcations of Central Configurations in the Four-Body Problem with Some Equal Masses
- Uniqueness results for co-circular central configurations for power-law potentials
- On polygonal relative equilibria in the N-vortex problem
- Stability of Relative Equilibria in the Planar $n$-Vortex Problem
- Isosceles trapezoid central configurations of the Newtonian four-body problem
- A note on the two nested regular polygonal central configurations
- Four-body co-circular central configurations
- On full-rank interval matrices
- Collision Singularities in Celestial Mechanics
- Symmetry of planar four-body convex central configurations
- Finiteness of stationary configurations of the four-vortex problem
- Regular Polygon Solutions of the N-Body Problem
- Stationary Configurations of Point Vortices
- Bifurcations of Relative Equilibria in the N-Body and Kirchhoff Problems
- The integral manifolds of the three body problem
- On the role and the properties ofn body central configurations
- Orbits of the Three-Body Problem Which Pass Infinitely Close to Triple Collision
- Relative equilibrium solutions in the four body problem
- On Clustering in Central Configurations
- Spectral instability of relative equilibria in the planarn-body problem
- The Apsides of General Dynamical Systems
- Strictly convex central configurations of the planar five-body problem
- Planar central configuration estimates in the n-body problem
- Central configurations of four bodies with one inferior mass
- Bifurcation of Spatial Central Configurations from Planar Ones