Expansion theory for the elliptic motion of arbitrary eccentricity and semi-major axis. VII - Elliptic expansions in terms of the sectorial variables for the seventh and eight categories

Details Expansion theory for the elliptic motion of arbitrary eccentricity and semi-major axis. VII - Elliptic expansions in terms of the sectorial variables for the seventh and eight categories Expansion theory for the elliptic motion of arbitrary eccentricity and semi-major axis. VII - Elliptic expansions in terms of the sectorial variables for the seventh and eight categories

May 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985ap%26ss.112...51s&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 112, no. 1, May 1985, p. 51-68.

Astronomy and Astrophysics

Astrophysics

6

Celestial Mechanics, Elliptical Orbits, Orbital Mechanics, Eccentric Orbits, Recursive Functions, Series Expansion, Trigonometric Functions

Scientific paper

In this paper of the series, elliptic expansions in terms of the sectorial variables θj(i) introduced recently in Paper IV (Sharaf, 1982) to regularise highly oscillating perturbations force of some orbital systems will be established analytically and computationally for the seventh and eighth 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.

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