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Notions of analytic vs numerical stability as applied to the numerical calculation of orbits

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Abstract

This paper deals with the implications of ‘stability’ as applied to the numerical calculation of orbits. The study was motivated by the recent appearance of several proposed transformations of the classical Newtonian equations of motion which ‘analytically stabilize’ Cowell's method. This report analyzes the basic properties of such stabilizing transformations and shows the removal of the period as a parameter is the key to these transformations and, that although such transformations do not yield global numerical error bounds, the error propagation properties are more favorable-linear vs quadratic growth.

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  1. Systems Development and Analysis Branch, Mission Support Computing and Analysis Division, NASA/Goddard Space Flight Center, Greenbelt, Md., USA

    C. E. Velez

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  1. C. E. Velez
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Velez, C.E. Notions of analytic vs numerical stability as applied to the numerical calculation of orbits. Celestial Mechanics 10, 405–422 (1974). https://doi.org/10.1007/BF01229118

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  • DOI: https://doi.org/10.1007/BF01229118

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