LINEAR STABILITY IN THE 1 + N-GON RELATIVE EQUILIBRIUM

DOI10.1142/9789812792099_0018zbMath1022.70007OpenAlexW1963611475MaRDI QIDQ2724639

Gareth E. Roberts

Publication date: 30 October 2003

Published in: Hamiltonian Systems and Celestial Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/9789812792099_0018

zbMATH Keywords

linear stability\(n\)-body problemrelative equilibriumregular \(n\)-gonMoeckel conjecture

Mathematics Subject Classification ID

Celestial mechanics (70F15) (n)-body problems (70F10) Stability problems for problems in Hamiltonian and Lagrangian mechanics (70H14)

Related Items (20)

BIFURCATIONS FROM PLANAR TO THREE-DIMENSIONAL PERIODIC ORBITS IN THE RING PROBLEM OF N BODIES WITH RADIATING CENTRAL PRIMARY ⋮ On the symmetric central configurations for the planar \(1+5\)-body problem with small arbitrary masses ⋮ Linear stability of the \(n\)-gon relative equilibria of the \((1+n)\)-body problem ⋮ On the central configurations of the planar 1 + 3 body problem ⋮ Global bifurcation of planar and spatial periodic solutions in the restricted \(n\)-body problem ⋮ Structure and stability of the rhombus family of relative equilibria under general homogeneous forces ⋮ On the symmetric central configurations of three coorbital satellites ⋮ Global bifurcation of polygonal relative equilibria for masses, vortices and dNLS oscillators ⋮ Braids of the N-body problem I: cabling a body in a central configuration ⋮ Planar \(N\)-body central configurations with a homogeneous potential ⋮ Periodic motions and their stability in a \(N=\nu+1\)-body regular polygonal configuration ⋮ Bifurcation of central configuration in the \(2N+1\) body problem ⋮ Symmetries and choreographies in families that bifurcate from the polygonal relative equilibrium of the \(n\)-body problem ⋮ Collision index and stability of elliptic relative equilibria in planar \(n\)-body problem ⋮ Linear stability of the elliptic relative equilibrium with (1  +  n)-gon central configurations in planar n-body problem ⋮ Existence, Stability, and Symmetry of Relative Equilibria with a Dominant Vortex ⋮ Applying the symmetry groups to study the \(n\) body problem ⋮ On the symmetric central configurations for the planar \(1+4\)-body problem ⋮ Bifurcation of Relative Equilibria of the (1+3)-Body Problem ⋮ A note on the relative equilibria bifurcations in the \((2N+1)\)-body problem

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