Expansion theory for the elliptic motion of arbitrary eccentricity and semi-major axis . V - Elliptic expansions in terms of the sectorial variables for the first four categories

Details Expansion theory for the elliptic motion of arbitrary eccentricity and semi-major axis . V - Elliptic expansions in terms of the sectorial variables for the first four categories Expansion theory for the elliptic motion of arbitrary eccentricity and semi-major axis . V - Elliptic expansions in terms of the sectorial variables for the first four categories

Jun 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983ap%26ss..93..377s&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 93, no. 2, June 1983, p. 377-401.

Astronomy and Astrophysics

Astrophysics

8

Celestial Mechanics, Elliptical Orbits, Orbit Perturbation, Orbital Mechanics, Series Expansion, Astronomical Coordinates, Axes Of Rotation, Coordinate Transformations, Eccentric Orbits, Orbital Elements, Regularity, Sectors, Trigonometric Functions

Scientific paper

Sharaf (1982) proposed a regularization method for the oscillating functions of some natural and artificial orbital systems for which the conventional methods of general perturbations yield divergent, or at least weakly convergent, series in the solutions of their motions. This method was developed as far as a formulation of treatments with the novel 'elliptic sector' unit. Attention is presently given to the expansions of elliptic coordinates, and functions of the coordinates, in terms of the sectorial variables. For each of the elliptic expansions belonging to a category, literal analytical expressions for the trigonometric series representation coefficients are established. Recurrence formulae satisfied by these coefficients are also given, to facilitate computation, and numerical results are included in order to provide test examples for the construction of computational algorithms.

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