Accurate integration of geostationary orbits with Burdet's focal elements

Details Accurate integration of geostationary orbits with Burdet's focal elements Accurate integration of geostationary orbits with Burdet's focal elements

Sep 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975ap%26ss..36..495f&link_type=abstract

Astrophysics and Space Science, vol. 36, Sept. 1975, p. 495-503.

Mathematics

3

Boundary Value Problems, Harmonic Oscillators, Numerical Integration, Orbital Elements, Stationary Orbits, Two Body Problem, Coordinate Transformations, Eccentric Orbits, Perturbation Theory, State Vectors, Synchronous Satellites, Vectors (Mathematics)

Scientific paper

The theory of Burdet's focal elements (1969) 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 and 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, Kustaanheimo-Stiefel (1971) theory, and rectangular coordinates. For this class of orbits, a higher accuracy has been obtained by integrating elements than integrating rectangular coordinates.

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