Mathematics
Scientific paper
Dec 1974
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974cemec..10..451j&link_type=abstract
Celestial Mechanics, vol. 10, Dec. 1974, p. 451-467.
Mathematics
9
Artificial Satellites, Eccentric Orbits, Orbit Calculation, Orbit Perturbation, Satellite Orbits, Cartesian Coordinates, Equations Of Motion, Error Analysis, Independent Variables, Numerical Integration, Perturbation Theory, Runge-Kutta Method, Transformations (Mathematics)
Scientific paper
For computing highly eccentric (e greater than or about equal to 0.9) earth satellite orbits with special perturbation methods, a comparison is made between different schemes - namely, the direct integration of the equations of motion in Cartesian coordinates, changes of the independent variable, use of a time element, stabilization, and use of regular elements. A one-step and a multistep integration are also compared. It is shown that stabilization and regularization procedures are very helpful for unperturbed or smoothly perturbed orbits. In practical cases for space research where all perturbations are considered, these procedures are no longer so efficient. The recommended method in these cases is a multistep integration of the Cartesian coordinates with a change of the independent variable defining an analytical step size regulation. However, the use of a time element and a stabilization procedure for the equations of motion improves the accuracy, except when a small step size is chosen.
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