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

Abstract

In this paper of the series, elliptic expansions in terms of the sectorial variablesθ ⁽ⁱ⁾ _j introduced recently in Paper IV (Sharaf, 1982) to regularize highly oscillating perturbations force of some orbital systems will be established analytically and computationally for the fifth and sixth categories. 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 computations; numerical results are included to provide test examples for constructing computational algorithms.