Expansion theory for 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 |
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| Abstract: | In this paper of the series, we arrive at the end of the second step of our regularization approach, and in which, elliptic expansions in terms of the sectorial variables 
j
(i)
introduced by the author in Paper IV (Sharaf, 1982b) to regularize the highly oscillating perturbation force of some orbital systems will be established analytically and computationally for the thirteenth, fourteenth, fifteenth, and sixteenth 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 analytic 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 computations, and numerical results are included to provide test examples for constructing computational algorithms. Finally, the second and the last collection of completed elliptic expansion will be given in Appendix B, such that, the materials of Appendix A of Paper VIII (Sharaf, 1985b) and those of Appendix B of the present paper provide the reader with the elliptic expansions in terms of
j
(i)
so explored for the second step of our regularization approach. |
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