A Second-Order Global Solution of the Ideal Resonance Problem

Details A Second-Order Global Solution of the Ideal Resonance Problem A Second-Order Global Solution of the Ideal Resonance Problem

Mar 1974

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974cemec...9..105g&link_type=abstract

Celestial Mechanics, Volume 9, Issue 1, pp.105-125

Physics

12

Scientific paper

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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