Maslov-type indices and linear stability of elliptic Euler solutions of the three-body problem

Abstract

In this paper, we use the central configuration coordinate decomposition to study the linearized Hamiltonian system near the elliptic Euler solutions. Then using the Maslov-type ω-index theory of symplectic paths and the theory of linear operators we compute the ω-indices and obtain certain properties of linear stability of the Euler elliptic solutions of the classical three-body problem.

42 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1206.6162; text overlap with arXiv:1308.4745 by other authors

References in corpus (3)

• Collision index and stability of elliptic relative equilibria in planar n-body problem
• Maslov-type indices and linear stability of elliptic Euler solutions of the three-body problem
• The reduction on the linear stability of elliptic Euler-Moulton solutions of the n-body problem to those of 3-body problems

Cited by in corpus (10)

• Maslov-type indices and linear stability of elliptic Euler solutions of the three-body problem
• Linear stability of the elliptic relative equilibrium with $(1+n)$-gon central configurations in planar $n$-body problem
• Linear Stability of Elliptic Relative Equilibria of Restricted Four-body Problem
• Trace estimation of a family of periodic Sturm-Liouville operators with application to Robe's restricted three-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
• The analytical aspect to the linear stability of elliptic equilibrium points of the Robe's restricted three-body problem
• The symplectic reduction of the linearized Hamiltonian systems at elliptic relative equilibria of four-body problem
• Hill-type formula for Hamiltonian system with Lagrangian boundary conditions
• Linear stability of the elliptic relative equilibria for the restricted N-body problem: two special cases