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Universal Keplerian state transition matrix

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Abstract

A completely general method for computing the Keplerian state transition matrix in terms of Goodyear's universal variables is presented. This includes a new scheme for solving Kepler's problem which is a necessary first step to computing the transition matrix. The Kepler problem is solved in terms of a new independent variable requiring the evaluation of only one transcendental function. Furthermore, this transcendental function may be conveniently evaluated by means of a Gaussian continued fraction.

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Authors and Affiliations

  1. The Charles Stark Draper Laboratory, Inc., Cambridge, Mass., USA

    Stanley W. Shepperd (Staff Member, Guidance and Navigation Analysis Division)

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  1. Stanley W. Shepperd
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This work was supported at The Charles Stark Draper Laboratory, Inc., by the National Aeronautics and Space Administration under Contract NAS9-16023.

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Shepperd, S.W. Universal Keplerian state transition matrix. Celestial Mechanics 35, 129–144 (1985). https://doi.org/10.1007/BF01227666

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  • DOI: https://doi.org/10.1007/BF01227666

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