Astronomy and Astrophysics – Astronomy
Scientific paper
Sep 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994cemda..60...69b&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, vol. 60, no. 1, p. 69-89
Astronomy and Astrophysics
Astronomy
10
Anomalies, Eccentricity, Elliptic Functions, Elliptical Orbits, Orbit Calculation, Orbital Mechanics, Hypergeometric Functions, Polynomials, Recursive Functions, Two Body Problem
Scientific paper
New expansions of elliptic motion based on considering the eccentricity e as the modulus k of elliptic functions and introducing the new anomaly w (a sort of elliptic anomaly) defined by w = ((piu)/2k) - (pi/2), g = ((am)(u)) - (pi/2) (g being the eccentric anomaly) are compared with the classic (e,M), (e,v) and (e,g) expansions in multiples of mean, true and eccentric anomalies, respectively. These (q,w) expansions turn out to be in general more compact than the classical ones. The coefficients of the (e,v) and (e,g) expansions are expressed as the hypergeometric series, which may be reduced to the hypergeometric polynomials. The coefficients of the (q,w) expansions may be presented in closed (rational function) form with respect to q, k, k' = square root of (1 - k2), K and E, q being the Jacobi nome related k while K and E are the complete elliptic integrals of the first and second kind respectively. Recurrence relations to compute these coefficients have been derived.
Brumberg Eugene
Fukushima Toshio
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