EXPANSIONS OF ELLIPTIC MOTION BASED ON ELLIPTIC FUNCTION-THEORY

New expansions of elliptic motion based on considering the eccentricit y e as the modulus k of elliptic functions and introducing the new ano maly 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 clas sic (e, M), (e, v) and (e, g) expansions in multiples of mean, true an d eccentric anomalies, respectively. These (q, w) expansions turn out to be in general more compact than the classical ones. The coefficient s of the (e, v) and (e, g) expansions are expressed as the hypergeomet ric series, which may be reduced to the hypergeometric polynomials. Th e coefficients of the (q, w) expansions may be presented in closed (ra tional function) form with respect to q, k, k' = (1 - k2)1/2, K and E, q being the Jacobi nome related k while K and E are the complete elli ptic integrals of the first and second kind respectively. Recurrence r elations to compute these coefficients have been derived.