Astronomy and Astrophysics – Astrophysics
Scientific paper
Apr 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981ap%26ss..75..437l&link_type=abstract
Astrophysics and Space Science, vol. 75, no. 2, Apr. 1981, p. 437-454.
Astronomy and Astrophysics
Astrophysics
Celestial Mechanics, Elliptic Functions, Orbit Calculation, Three Body Problem, Differential Equations, Hamilton-Jacobi Equation, Integral Equations, Perturbation Theory
Scientific paper
The restricted three-body Hamiltonian is partitioned into a two-center type principal part and its accompanying perturbational part. The mathematical analysis, involving the Jacobian elliptic function, is adapted for the case of figure-eight orbits winding around the two given mass points. For many such orbits the elliptic function modulus k is small and can serve as a small parameter. Fourier expansions in terms of a parameter related to t are obtained for the intermediate orbit functions which provide representations in terms of elementary functions.
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