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Barrabés Vera, Esther
Cors, Josep M. Pinyol i Pérez, Concepció Soler, Jaume |
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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 | |
| http://hdl.handle.net/2072/207211 | |
| eng | |
| Elsevier | |
| Tots els drets reservats | |
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Topologia
Topology Poliedres Polyhedra |
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| Highly eccentric hip-hop solutions of the 2N | |
| info:eu-repo/semantics/article | |
| Recercat |
