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

VIII. Elliptic expansions in terms of the sectorial variables for the ninth, tenth, eleventh, and twelfth categories

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Abstract

In this paper of the series, elliptic expansions in terms of the sectorial variables θ j (i) introduced by the author in Paper IV (Sharaf, 1982) to regularize the highly oscillating perturbation force of some orbital systems will be established analytically and computationally for the ninth, tenth, eleventh, and twelfth categories according to our adopted scheme of presentation drawn up in Paper V (Sharaf, 1983). For each of the elliptic expansions belonging to a category, literal analytical expressions for the coefficients of its trigonometric series representation are established. Moreover, some recurrence formulae satisfied by these coefficients are also established to facilitate their computation, and numerical results are included to provide test examples for constructing computational algorithms. Finally, the first collection of completed elliptic expansions in terms of θ j (i) so explored will be given in Appendix A for the guidance of the reader.

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References

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Sharaf, M.A. Expansion theory for the elliptic motion of arbitrary eccentricity and semi-major axis. Astrophys Space Sci 116, 251–283 (1985). https://doi.org/10.1007/BF00653782

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  • DOI: https://doi.org/10.1007/BF00653782

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