Abstract
view Abstract Citations (43) References (7) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A Recursive von Zeipel Algorithm for the Ideal Resonance Problem Garfinkel, Boris ; Jupp, Alan ; Williams, Carol Abstract The Ideal Resonance Problem is defined by the Hamiltonian F=B(y)+2eA(y) 5in2X, E 1. A recursive algorithm is constructed here for generating a solution of the problem to any order in e by means of the Bohlin-von Zeipel technique. The solution is valid in the entire phase plane, including asymp- totically the classical limit at infinity. All the singularities have been suppressed by a proper choice of a new Hamiltonian Fj', involving the special function ss' expE- (k/k')i+1], where k is the elliptic modulus, and k2+k'2- 1. As an illustration, the algorithm is used to generate a solution of the first order in E . This solution corrects and supersedes the one published previously by Garfinkel (1966). Publication: The Astronomical Journal Pub Date: March 1971 DOI: 10.1086/111099 Bibcode: 1971AJ.....76..157G full text sources ADS | Related Materials (1) Erratum: 1971AJ.....76..581G
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