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Título:
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Highly eccentric hip-hop solutions of the 2N
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Autor/a:
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Barrabés Vera, Esther; Cors, Josep M.; Pinyol i Pérez, Concepció; Soler, Jaume
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Abstract:
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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 |
Materia(s):
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-Topologia -Topology -Poliedres -Polyhedra |
Derechos:
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Tots els drets reservats |
Tipo de documento:
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Artículo Artículo - Versión aceptada |
Editor:
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Elsevier
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