Astronomy and Astrophysics – Astrophysics
Scientific paper
Jan 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981ap%26ss..74..211s&link_type=abstract
Astrophysics and Space Science, vol. 74, no. 1, Jan. 1981, p. 211-234. Research sponsored by the Science Research Council of Eng
Astronomy and Astrophysics
Astrophysics
13
Celestial Mechanics, Eccentric Orbits, Elliptical Orbits, Fourier Series, Orbital Mechanics, Algorithms, Orbit Perturbation, Orbital Elements, Recursive Functions, Set Theory
Scientific paper
In this paper of the series, literal analytical expressions for the coefficients of the Fourier series representation of F will be established for any x; with n, N positive integers ~1 and ~ < 1 for i 1, 2,... n. Moreover, the recurrence formulae satisfied by these coefficients will also be established. Illustrative analytical examples and a full recursive computational algorithm, with its numerical results, are included. The applications of the recurrence formulae are also illustrated by their stencils. As a by-product of the analyses is an integral which we may call a complete elliptic integral of the nth kind, in which the known complete elliptic integrals (1st, 2nd and 3rd kinds) are special cases of it
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