caa a22 4500 467986983 CHVBK 20180323112534.0 cr unu---uuuuu 170328e19900601xx s 000 0 eng 10.1007/BF00050715 doi (NATIONALLICENCE)springer-10.1007/BF00050715 Branham Jr. Richard Centro Regional de Investigaciones Cientificas y Technológicas, C.C.131, 5500, Mendoza, Argentina aut Recursive calculation of hansen coefficients [Elektronische Daten] [Richard Branham Jr.] Hansen coefficients are used in expansions of the elliptic motion. Three methods for calculating the coefficients are studied: Tisserand's method, the Von Zeipel-Andoyer (VZA) method with explicit representation of the polynomials required to compute the Hansen coefficients, and the VZA method with the values of the polynomials calculated recursively. The VZA method with explicit polynomials is by far the most rapid, but the tabulation of the polynomials only extends to 12th order in powers of the eccentricity, and unless one has access to the polynomials in machine-readable form their entry is laborious and error-prone. The recursive calculation of the VZA polynomials, needed to compute the Hansen coefficients, while slower, is faster than the calculation of the Hansen coefficients by Tisserand's method, up to 10th order in the eccentricity and is still relatively efficient for higher orders. The main advantages of the recursive calculation are the simplicity of the program and one's being able to extend the expansions to any order of the eccentricity with ease. Because FORTRAN does not implement recursive procedures, this paper used C for all of the calculations. The most important conclusion is recursion's genuine usefulness in scientific computing. Kluwer Academic Publishers, 1990 Elliptic motion expansion nationallicence Hansen coefficients nationallicence recursive procedure nationallicence Celestial Mechanics and Dynamical Astronomy Kluwer Academic Publishers 49/2(1990-06-01), 209-217 0923-2958 49:2<209 1990 49 10569 https://doi.org/10.1007/BF00050715 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00050715 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Branham Jr Richard Centro Regional de Investigaciones Cientificas y Technológicas, C.C.131, 5500, Mendoza, Argentina aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Kluwer Academic Publishers 49/2(1990-06-01), 209-217 0923-2958 49:2<209 1990 49 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer