Mathematics – Dynamical Systems
Scientific paper
Jun 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992cemda..53..151h&link_type=abstract
Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 53, no. 2, 1992, p. 151-183. Research supported by CEC.
Mathematics
Dynamical Systems
14
Asteroids, Jupiter (Planet), Orbital Resonances (Celestial Mechanics), Solar Orbits, Solar Planetary Interactions, Three Body Problem, Branching (Mathematics), Dynamical Systems, Elliptical Orbits, Hamiltonian Functions
Scientific paper
Four 3 : 1 resonant families of periodic orbits of the planar elliptic restricted three-body problem, in the sun-Jupiter-asteroid system, have been computed. Two of them, Ic, IIc bifurcate from the unstable region of the family of perodic orbits of the first kind (circular orbits of the asteroid) and are unstable and the other two, Ie, IIe, from the stable resonant 3 : 1 family of periodic orbits of the second kind (elliptic orbits of the asteroid). One of them is stable and the other is unstable. All the families of periodic orbits of the circular and the elliptic problem are compared with the corresponding fixed points of the averaged model used by several authors. The coincidence is good for the fixed points of the circular averaged model and the two families of the fixed points of the elliptic model corresponding to the families Ic, IIc, but is poor for the families Ie, IIe. A simple correction term to the averaged Hamiltonian of the elliptic model is proposed in this latter case, which makes the coincidence good.
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