A second-order global solution of the ideal resonance problem |
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Authors: | Boris Garfinkel Carol A Williams |
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Institution: | 1. Yale University Observatory, New Haven, Conn., U.S.A. 2. Dept. of Astronomy, University of South Florida Tampa, Fla., U.S.A.
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Abstract: | The Ideal Resonance Problem, as formulated in 1966 (Paper I), is defined by the Hamiltonian Following the procedure adopted in the construction of a first-orderglobal solution (Papers II, III, and V), we derive a second-order solution from the von Zeipel-Bohlin recursive algorithm of Paper II. The singularities inherent in the Bohlin expansion in powers of μ have been suppressed by means of theregularizing function of Paper III, and the singularities in the coefficients atAB″=0 have been removed by thenormalization technique of Paper V. As a check, it is shown that the global solution includes asymptotically theclassical solution, expanded in powers ofμ 2, and carrying thecritical divisor B′. |
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