Mathematics
Scientific paper
Jul 1980
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980cemec..22...13g&link_type=abstract
(Symposium on Star Catalogues, Positional Astronomy and Celestial Mechanics, Washington, D.C., Nov. 30, 1978.) Celestial Mechani
Mathematics
Librational Motion, Orbit Perturbation, Orbital Mechanics, Orbital Resonances (Celestial Mechanics), Resonance, Hamiltonian Functions, Poincare Problem, Quadratures, Singularity (Mathematics)
Scientific paper
Consideration is given to the use of the regularizing function in orbital resonance theory to remove the singularities associated with perturbations of all orders in a problem of simple resonance with a single near-commensurability of two of the fundamental frequencies of the motion. The intermediate Hamiltonian of the classical solution of the problem is formulated in terms of the Ideal Resonance Theory of Garfinkel (1976), and it is shown that the problem is then reducible to quadratures, with the critical argument undergoing libration. It is shown that the incorporation of the regularizing function introduced by Garfinkel (1977) into the undisturbed Hamiltonian can remove both the Poincare singularity at the turning points of the libration and the classical singularity at the center. It is noted, however, that the problem of double resonance remains unsolved.
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