The reducing transformation and apocentric librators

Details The reducing transformation and apocentric librators The reducing transformation and apocentric librators

Apr 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986cemec..38..335h&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 38, April 1986, p. 335-344.

Mathematics

25

Asteroids, Celestial Mechanics, Libration, Transformations (Mathematics), Degrees Of Freedom, Eccentricity, Jupiter (Planet), Orbit Perturbation, Three Body Problem

Scientific paper

A canonical transformation is proposed which reduces the averaged planetary problem near resonance to a one-degree-of-freedom problem when the perturbation is truncated at the first order in the eccentricities. This reducing transformation leads to a very simple explanation of the puzzling behavior of the apocentric librators, a class of asteroids identified by Franklin et al. (1975). An exploration of the phase space of the average problem with the use of the mapping technique shows that the alteration of two libration mechanisms is a common feature for initial conditions near, but not inside, the deep resonance region.

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