Symbolic solution of Kepler's generalized equation

Abstract

Kepler's generalized equation is a transcendental nonlinear equation that must be solved in order to compute the position and velocity of an artificial satellite at any instant t. In this paper, we propose a method to solve analytically that equation. The method is based on the properties of non canonical Lie transformations and, under certain conditions, it is shown that it gives better results than numerical methods. © Springer-Verlag Berlin Heidelberg 2003.