Computer Science
Scientific paper
Dec 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984cemec..34..411j&link_type=abstract
(Bundesministerium für Wissenschaft und Forschung of Austria, Alexander von Humboldt Colloguium on Celestial Mechanics: The Stab
Computer Science
10
Equations Of Motion, Hamiltonian Functions, Orbital Mechanics, Perturbation Theory, Resonance, Von Zeipel Method, Classical Mechanics, Elliptic Functions, Libration, Lie Groups, Numerical Integration, Series Expansion
Scientific paper
A comparison of Garfinkel's solution (1966) of the ideal resonance problem, derived from the techniques of Bohlin and von Zeipel, with Jupp's solution (1969), employing Poincare's action and angle variables and a procedure based on Lie series expansions, is discussed. Two different Hamiltonians are chosen for a comparison of the two theoretical solutions with the solutions obtained from direct numerical integrations of the differential equations of motion. The first-order theoretical solutions are given for the libration and circulation regions. It is shown that Jupp's solution is generally more accurate in deep resonance, while in the classical limit, Garfinkel's solution is in excellent agreement with the numerical integrations.
Abdulla A. Y.
Jupp Alan H.
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