The generalized Sundman transformation for propagation of high-eccentricity elliptical orbits
Berry, Matthew M.
Healy, Liam M.
in Alfriend, Neta, Luu, Hilton Walker, eds., Spaceflight Mechanics 2002, vol. 112 of Advances in the Astronautical Sciences, pp. 127-146
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A generalized Sundman transformation dt = cr^n ds for exponent n >= 1 may be used to accelerate the numerical computation of high-eccentricity orbits, by transforming time t to a new independent variable s. Once transformed, the integration in uniform steps of s effectively gives analytic step variation in t with larger time steps at apogee than at perigee, making errors at each point roughly comparable. In this paper, we develop techniques for assessing accuracy of s-integration in the presence of perturbations, and analyze the effectiveness of regularizing the transformed equations. A computational speed comparison is provided.
See also dissertation of Matt Berry at http://scholar.lib.vt.edu/theses/available/etd-04282004-071227/