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Increased accuracy of computations in the main satellite problem through linearization methods

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Abstract

The set of canonical redundant variables previously introduced by the first author is derived from Cartesian coordinates in a simplified form which allows the reduction of the Kepler problem to four harmonic oscillators with unit frequency. The coordinates are defined to be the direction cosines of the position of the particle along with the inverse of its distance. True anomaly is the new independent variable. The behavior of this new transformation is studied when applied to the numerical integrations of the main problem in satellite theory. In particular, computation time and accuracy of orbits in the new variables are compared with those in K-S and Cartesian variables. It is noteworthy that for high eccentricities the new variables require the least computation time for comparable accuracy, regardless of the integration scheme.

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Authors and Affiliations

  1. Dto. de Matemática Aplicada a la Ingenieria, E.T.S. Ingenieros Industriales, 47011, Valladolid, Spain

    Jose-Manuel Ferrándiz (Professor)

  2. Dto. de Matemática Aplicada a la Ingeniería, E.T.S. Ingenieros Industriales, 47011, Valladolid, Spain

    Maria-Eugenia Sansaturio (Associate Professor)

  3. Dept. of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, 78712, Austin, Texas, U.S.A.

    Joseph R. Pojman (Graduate Research Assistant)

Authors
  1. Jose-Manuel Ferrándiz
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  2. Maria-Eugenia Sansaturio
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  3. Joseph R. Pojman
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Ferrándiz, JM., Sansaturio, ME. & Pojman, J.R. Increased accuracy of computations in the main satellite problem through linearization methods. Celestial Mech Dyn Astr 53, 347–363 (1992). https://doi.org/10.1007/BF00051816

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  • DOI: https://doi.org/10.1007/BF00051816

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