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

Abstract

In this paper of the series, literal analytical expressions for the coefficients of the Fourier series representation ofG will be established for anyx _i; withn, N positive integers and |ξ_i|<1 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 by-products of the analyses are two important periodic integrals developed analytically and computationally.