The generalized Sundman transformation for propagation of high-eccentricity elliptical orbits

Berry, Matthew M.; Healy, Liam M.

The generalized Sundman transformation for propagation of high-eccentricity elliptical orbits

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Date

2002-01

Authors

Berry, Matthew M.

Healy, Liam M.

Citation

in Alfriend, Neta, Luu, Hilton Walker, eds., Spaceflight Mechanics 2002, vol. 112 of Advances in the Astronautical Sciences, pp. 127-146

Abstract

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.

Notes

See also dissertation of Matt Berry at http://scholar.lib.vt.edu/theses/available/etd-04282004-071227/

URI (handle)

http://hdl.handle.net/1903/3013

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