Expansion theory for the elliptic motion of arbitrary eccentricity and semi-major axis |
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| Authors: | Mohamed Adel Sharaf |
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| Institution: | (1) Dept. of Astronomy, University of Cairo, Egypt;(2) Present address: Earth Satellite Research Unit, Dept. of Mathematics, University of Aston in Birmingham, England |
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| Abstract: | In this paper of the series, literal analytical expressions for the coefficients of the Fourier series representation ofF will be established for anyx
i
; withn, N positive integers  1 and |
i
| fori=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 thenth kind, in which the known complete elliptic integrals (1st, 2nd and 3rd kinds) are special cases of it. |
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