Mathematics
Scientific paper
Sep 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987cemec..40..233y&link_type=abstract
Celestial Mechanics (ISSN 0008-8714), vol. 40, no. 3-4, 1987, p. 233-272.
Mathematics
33
Asteroid Belts, Astronomical Models, Resonance, Secular Variations, Canonical Forms, Eccentric Orbits, Hamiltonian Functions, Transformations (Mathematics)
Scientific paper
In this paper, the dynamics of the secular resonance nu6 is investigated by a simple analytical model, in which the third degree terms of the eccentricity and inclination are taken into account. The eccentricity variations of asteroids located near this resonance are represented clearly by the diagrams of equi-Hamiltonian curves on the plane of the longitude of perihelion of asteroids and Saturn versus the eccentricity of asteroids. These diagrams predict that the eccentricity of these asteroids suffers a large increase or decrease, and that the secular resonance argument (i.e., the longitude of perihelion of asteroids and Saturn) librates about 0 deg and 180 deg. In order to confirm these predictions, numerical integrations are carried out over one million years. By these integrations, it is found that the eccentricity of secular resonant asteroids becomes more than 0.8, and that the libration about 0 deg also exists, as well as the libration about 180 deg.
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