Item


Highly eccentric hip-hop solutions of the 2N

We show the existence of families of hip-hop solutions in the equal-mass 2N-body problem which are close to highly eccentric planar elliptic homographic motions of 2N bodies plus small perpendicular non-harmonic oscillations. By introducing a parameter ϵ, the homographic motion and the small amplitude oscillations can be uncoupled into a purely Keplerian homographic motion of fixed period and a vertical oscillation described by a Hill type equation. Small changes in the eccentricity induce large variations in the period of the perpendicular oscillation and give rise, via a Bolzano argument, to resonant periodic solutions of the uncoupled system in a rotating frame. For small ϵ ≠ 0, the topological transversality persists and Brouwer’s fixed point theorem shows the existence of this kind of solutions in the full system

© Physica D: Nonlinear Phenomena, 2010, vol. 239, núm. 3-4, p. 214-219

Elsevier

Author: Barrabés Vera, Esther
Cors, Josep M.
Pinyol i Pérez, Concepció
Soler, Jaume
Date: 2009
Abstract: We show the existence of families of hip-hop solutions in the equal-mass 2N-body problem which are close to highly eccentric planar elliptic homographic motions of 2N bodies plus small perpendicular non-harmonic oscillations. By introducing a parameter ϵ, the homographic motion and the small amplitude oscillations can be uncoupled into a purely Keplerian homographic motion of fixed period and a vertical oscillation described by a Hill type equation. Small changes in the eccentricity induce large variations in the period of the perpendicular oscillation and give rise, via a Bolzano argument, to resonant periodic solutions of the uncoupled system in a rotating frame. For small ϵ ≠ 0, the topological transversality persists and Brouwer’s fixed point theorem shows the existence of this kind of solutions in the full system
Format: application/pdf
ISSN: 0167-2789
Document access: http://hdl.handle.net/10256/7552
Language: eng
Publisher: Elsevier
Collection: Versió postprint del document publicat a: http://dx.doi.org/10.1016/j.physd.2009.10.019
Articles publicats (D-IMA)
Is part of: © Physica D: Nonlinear Phenomena, 2010, vol. 239, núm. 3-4, p. 214-219
Rights: Tots els drets reservats
Subject: Topologia
Topology
Poliedres
Polyhedra
Title: Highly eccentric hip-hop solutions of the 2N
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

Subjects

Authors