Statistics – Methodology
Scientific paper
Nov 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..28..275g&link_type=abstract
Celestial Mechanics, vol. 28, Nov. 1982, p. 275-290.
Statistics
Methodology
11
Celestial Mechanics, Equations Of Motion, Gas Giant Planets, Resonance, Hamiltonian Functions, Jupiter (Planet), Neptune (Planet), Perturbation Theory, Pluto (Planet), Saturn (Planet), Solar System
Scientific paper
The theory of resonance in celestial mechanics is discussed, beginning with the genesis of the small divisor. It is noted that the fundamental distinction between the shallow and deep resonance is illustrated by the 5:2 Jupiter-Saturn and the 3-2 Neptune-Pluto resonances in the planetary system. The search for a global solution through a removal of the small divisor is treated historically by considering the work of Laplace, Bohlin, and Poincare. The contribution made by the author to the methodology is the formulation and solution of the ideal resonance problem. When the resonance is simple, all the singularities in the solution are removed by means of a regularizing function. If, on the other hand, the resonance is double, the second critical divisor is seen as irremovable, and a global solution may be precluded.
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