arXiv Analytics

Sign in

arXiv:1510.06822 [math.DS]AbstractReferencesReviewsResources

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

Qinglong Zhou, Yiming Long

Published 2015-10-23Version 1

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 \omega-index theory of symplectic paths and the theory of linear operators we compute the \omega-indices and obtain certain properties of linear stability of the Euler elliptic solutions of the classical three-body problem.

Comments: 37 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1206.6162; text overlap with arXiv:1308.4745 by other authors
Categories: math.DS, math-ph, math.MP, math.SG
Subjects: 58E05, 37J45, 34C25
Related articles: Most relevant | Search more
arXiv:1206.6162 [math.DS] (Published 2012-06-27, updated 2014-01-27)
Linear stability of elliptic Lagrangian solutions of the planar three-body problem via index theory
arXiv:1806.01641 [math.DS] (Published 2018-06-02)
Linear Stability of Elliptic Rhombus Solutions of the Planar Four-body Problem
arXiv:1511.00070 [math.DS] (Published 2015-10-31)
The linear stability of elliptic Euler-Moulton solutions of the n-body problem via those of 3-body problems

Links

Toolbox