Accurate integration of geostationary orbits with Burdet's focal elements

The theory of Burdet's focal elements is outlined. The differential equations are presented, and the initial value problem is described together with the transformation to rectangular coordinates and classical elements. The focal elements are well defined for zero eccentricity and inclination. They can be adopted for the computation of elliptic, parabolic and hyperbolic motion. For the numerical integration of near-geostationary orbits a comparison of the efficiency is made between focal elements, KS theory and rectangular coordinates. For this class of orbits, a higher accuracy has been obtained by integrating elements than integrating rectangular coordinates.