Abstract
This paper is a sequel to an earlier article of the same title. The two formal analytical solutions of the Ideal Resonance Problem developed respectively by Garfinkel and Jupp are here compared, atsecond-order in the appropriate small parameter, with numerical integrations; the second-order circulation solution for Jupp's theory being presented for the first time. It transpires that throughout most of the deep resonance regime the second-mentioned solution provides greater accuracy. In addition, it is demonstrated that the first solution is not appropriate when general initial values of the variables are prescribed.
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References
Garfinkel, B.: 1966,Astron. J. 71, 657 (I).
Garfinkel, B., Jupp, A.H., and Williams, C.: 1971,Astron. J. 76, 157 (II).
Garfinkel, B. and Williams, G.: 1974,Celest, Mech,9, 105 (III).
Jupp, A. H.: 1969,Astron. J. 74, 35 (I′).
Jupp, A. H.: 1970,Monthly Notices Roy. Astron. Soc. 148, 197 (II′).
Jupp, A. H.: 1972,Celest. Mech. 5, 8 (III′).
Jupp, A. H.: 1982,Celest. Mech. 26, 413.
Jupp, A. H.: 1984,Celest. Mech. 34, 411 (IV').
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Jupp, A.H., Abdulla, A.Y. The ideal resonance problem, a comparison of two formal solutions, II. Celestial Mechanics 37, 183–197 (1985). https://doi.org/10.1007/BF01230927
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DOI: https://doi.org/10.1007/BF01230927