Families of Periodic Orbits Emanating From Homoclinic Orbits in the Restricted Problem of Three Bodies

Authors: Henrard, Jacques¹; Navarro, Juan²

Source: Celestial Mechanics and Dynamical Astronomy, Volume 89, Number 3, July 2004 , pp. 285-304(20)

Publisher: Springer

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Abstract:

We describe and comment the results of a numerical exploration on the evolution of the families of periodic orbits associated with homoclinic orbits emanating from the equilateral equilibria of the restricted three body problem for values of the mass ratio larger than μ ₁. This exploration is, in some sense, a continuation of the work reported in Henrard [Celes. Mech. Dyn. Astr. 2002, 83, 291]. Indeed it shows how, for values of μ. larger than μ ₁, the Trojan web described there is transformed into families of periodic orbits associated with homoclinic orbits. Also we describe how families of periodic orbits associated with homoclinic orbits can attach (or detach) themselves to (or from) the best known families of symmetric periodic orbits.

Keywords: bifurcations; homoclinic orbits; periodic orbits; restricted three body problem

Document Type: Research article

DOI: http://dx.doi.org/10.1023/B:CELE.0000038608.06392.e0

Affiliations: 1: Department of Mathematics, University of Namur, 8 Rempart de la Vierge, B-5000, Namur, Belgium, Email: jacques.henrard@fundp.ac.be 2: Depto de Matemática A., University of Alicante, P.O. Box 99, E-03080, Alicante, Spain,

Publication date: 2004-07-01