Abstract
The precise numerical integration of Cowell's equations of satellite motion is frequently performed with an independent variables defined by an equation of the form dt=cr nds, wheret represents time,r the radial distance from the center of attraction,c is a constant, andn is a parameter. This has been primarily motivated by the ‘uniformizing’ effects of such a transformation resulting in desirable ‘analytic’ stepsize control for elliptical orbits. This report discusses the ‘proper’ choice of the parametern defining the independent variables for various types of orbits and perturbation models, and develops a criterion for its selection.
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References
Baumgarte, J.: 1971,Celest. Mech. 5, 490.
Cappellari, J., Velez, C., and Fuchs, A.: 1976, ‘Mathematical Theory of the Goddard Trajectory Determination System’, NASA X-Document, X-582-76-77.
Feagin, T. and Mikkilineni, R.: 1978, to appear inCelest. Mech.
Henrici, P.: 1963,Error Propagation for Difference Methods, John Wiley.
Merson, R.: 1975, ‘Numerical Integration of the Differential Equations of Celestial Mechanics’, Royal Aircraft Establishment TR 74184.
Nacozy, P.: 1978, to appear inCelest. Mech.
Velez, C.: 1974,Celest. Mech. 10, 405.
Velez, C. and Maury, J.: 1970, ‘Derivation of Newtonian-Type Integration Coefficients and Some Applications to Orbit Calculations’, NASA TN D-5958.
Wong, P.: 1972,Some Special Perturbation Methods for the Integration of Artificial Satellite Orbits, UCLA Doctoral Dissertation (available from University Microfilms, Ann Arbor, Michigan, No. 72-20, 485).
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Velez, C.E., Hilinski, S. Time transformations and Cowell's method. Celestial Mechanics 17, 83–99 (1978). https://doi.org/10.1007/BF01261054
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DOI: https://doi.org/10.1007/BF01261054