Linear stability of the elliptic relative equilibrium with $(1+n)$-gon central configurations in planar $n$-body problem

Abstract

We study the linear stability of $(1+n)$-gon elliptic relative equilibrium (ERE for short), that is the Kepler homographic solution with the $(1+n)$-gon central configurations. We show that for $n\ge 8$ and any eccentricity $e\in [0,1)$, the $(1+n)$-gon ERE is stable when the central mass $m$ is large enough. Some linear instability results are given when $m$ is small.

arXiv comment28 pages, 3 figures

References in corpus (5)

• Some Problems on the Classical N-Body Problem
• Linear Stability of Ring Systems
• Morse index and linear stability of the Lagrangian circular orbit in a three-body-type problem via index theory
• Collision index and stability of elliptic relative equilibria in planar n-body problem
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Cited by in corpus (5)

• Linear Stability of Elliptic Relative Equilibria of Restricted Four-body Problem
• Linear stability of elliptic relative equilibria of four-body problem with two infinitesimal masses
• Linear Instability of Elliptic Rhombus Solutions to the Planar Four-body Problem
• A natural decomposition of the Jacobi equation for some classes of $N$-body problems
• Linear stability of the elliptic relative equilibria for the restricted N-body problem: two special cases