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Relative Behavior Of Special Algorithms For The Numerical Integration Of Satellite Orbits
Pablo Martin and Jose M. Ferriandiz*
Abstract
The purpose of this paper is to report on the relative performance of some of the various special algorithms designed for the numerical integration of satellite orbits, paying particular attention to those that have been introduced, or frequently quoted, in the recent lit-erature. Among them, we have first chosen the well known multistep codes by Bettis or the new SMF ones, which require taking the equations of motion into oscillator form - for instance by means of the KS or BF transformations. Besides them, the symplectic algo-rithms have been considered, since a number of papers have been published about them in the last years, mainly in numerical analysis journals, but they have not been sufficiently tested yet in the context of orbital dynamics problems. We have also found it timely to consider the power series methods, that have been the topic of several recent papers, and to their natural competitor, the Scheifele G-functions algorithm. For all the former methods, a number of numerical experiments have been made concerning the propagation of Earth satellite orbits. The preference has been assigned to low eccentricities and reduced, but quite representative, sets of pertur-bations although results for highly eccentric cases are also included
so that the possibilities of the different methods can be appreciated
better. As reference numerical algorithms we have used the very efficient Adams codes with fixed step-size or the RK7(8) with automatic error control.
Finally, we take up the question of the choice between either formu-lating the dynamical problem in terms of elements and using stan-dard numerical methods or integrating by means of special codes, that have usually been developed for sets of coordinates. Examples of long-term propagation of orbits are offered showing that the second possibility can give the better results in ordinary cases and therefore the research on special algorithms is worthwhile.
*E.T.S de Ingenieros Industriales Paseo del cauce s/n Universidad de Valladolid E-47011 Valladolid Spain.