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Expansion theory for the elliptic motion of arbitrary eccentricity and semi-major axis

III. Analytical and computational developments of the functions\(\begin{gathered} H_1^{(m)} (\varepsilon ,\theta ) = \cos {\text{ }}m \{ cos^{ - 1} (1 - \varepsilon {\text{ sin}}^2 \theta )\} ; H_2 (\varepsilon ,\xi ,\theta ) = {\text{ log \{ }}1 - \xi + \xi \varepsilon {\text{ sin}}^2 \theta {\text{\} ;}} \hfill \\ H_3^{(q)} (\varepsilon ,\xi ,\theta ) = {\text{\{ }}1 - \xi + \xi \varepsilon {\text{ sin}}^2 \theta {\text{\} }}^q \hfill \\ \end{gathered}\)

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Abstract

In this paper of the series, the expansions of the functionsH 1,H 2, andH 3 will be established analytically and computationally form positive integer,q any real number and ξ, ɛ are both positive <1. Full recursive computational algorithms with their numerical results will also be included.

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References

  • Sharaf, M. A.: 1981,Astrophys. Space Sci. 74, 211.

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  • Smart, W. M.: 1953,Celestial Mechanics, Longmans, Green and Co. Ltd., London.

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  1. Mohamed Adel Sharaf

    Present address: Earth Satellite Research Unit, Department of Mathematics, University of Aston in Birmingham, England

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  1. Dept. of Astronomy, University of Cairo, Egypt

    Mohamed Adel Sharaf

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  1. Mohamed Adel Sharaf
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Adel Sharaf, M. Expansion theory for the elliptic motion of arbitrary eccentricity and semi-major axis. Astrophys Space Sci 84, 53–71 (1982). https://doi.org/10.1007/BF00713627

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  • DOI: https://doi.org/10.1007/BF00713627

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