The ideal resonance problem, a comparison of two formal solutions. II

Physics

Scientific paper

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Analytic Functions, Resonance, Theoretical Physics, Boundary Value Problems, Libration

Scientific paper

The second-order circulation solution for Jupp's theory (1972) is presented, and compared with the second-order formal analytical solution of the ideal resonance problem developed by Garfinkel et al. (1971), in the appropriate small parameter, with numerical integrations. Comparison for two specific choices of Hamiltonian indicates that Jupp's solution provides greater accuracy throughout most of the deep-resonance regime, while in the classical limit remote from the resonance domain, Garfinkel's solution is found to be in excellent agreement with the numerical solution and Jupp's solution is quite unsatisfactory. In addition, it is shown that Garfinkel's solution is not appropriate when general initial values of the variables are prescribed.

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