Título:
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Highly eccentric hip-hop solutions of the 2N-body problem
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Autor/a:
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Barrabés Vera, Esther; Cors Iglesias, Josep Maria; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
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Otros autores:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II |
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 Є, 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 Є ≠ 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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-Àrees temàtiques de la UPC::Enginyeria mecànica -Many-body problem -Oscillations -Problema dels cossos múltiples -Oscil·lacions -Classificació AMS::70 Mechanics of particles and systems::70F Dynamics of a system of particles, including celestial mechanics |
Derechos:
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Tipo de documento:
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Artículo - Versión presentada Artículo |
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