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Stabilization and Real World Satellite Problem

  • C. E. Velez
Conference paper
Part of the COSPAR-IAU-IUTAM book series (IUTAM)

Abstract

Many recent investigations have concerned themselves with the development of transformations which tend to “dynamically stabilize”, “regularize”, or otherwise “smooth” the classical Newtonian equations of unperturbed motion with the goal of improving the numerical behavior of the system for the perturbed case. Examples of such transformations include stabilization by the application of integrals, independent variable transformations, and dependent variable transformations for the case of highly perturbed motion. The specific transformations examined include the energy control term and element equations developed by Stiefel, Scheifele and Baumgarte, and time regularization techniques.

It is shown by computer simulations of several NASA satellite orbits that in many cases, while such transformations do tend to improve the error growth properties of the perturbed problem, they do so at an added expense which degrades the overall efficiency. It is further shown that this results from adverse effects these transformations have on (i) the numerical stability regions of the integrator, or (ii) local error uniformity, or (iii) formulation “overhead”. It is concluded that while such transformations may allow one to attain high precision results which are otherwise unattainable in classical formulations, with the exception of analytic stepsize control, they offer little or no advantage over the classical methods in the intermediate accuracy range, when overall efficiency is considered.

Keywords

Control Term Local Truncation Error True Anomaly Orbit Generator Time Regularize 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Velez, C.: Notions of Analytic vs. Numerical Stability as Applied to the Numerical Integration of Orbits. Presented at the AIAA/AAS Astrodynamics Conference, Vail, Colorado, July 1973, to appear in Celestial Mechanics.Google Scholar
  2. 2.
    Long, A.; Nimitz, K.; Cefola, P.: The Next Generation of Orbit Prediction Formulations for Artificial Satellites II. CSC, 9101–14600–01TR, March 1973.Google Scholar
  3. 3.
    Stiefel, E.; Scheifele, G.: Linear and Regular Celestial Mechanics. New York: Springer-Verlag 1971.zbMATHGoogle Scholar
  4. 4.
    Baumgarte, J.: Dynamic Stabilization of Perturbed Keplerian Motions. Celestial Mechanics 5 (1972) 490.MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Baumgarte, J.; Stiefel, E.: Celestial Mechanics (1974) in press.Google Scholar
  6. 6.
    Moore, W.; Beaudet, P.: The Testing of Fixed-Step Numerical Integration Processes for the Cowell Method of Special Perturbations. Proceeding of the Conference on the Numerical Solution of Ordinary Differential Equations, v. 362. Heidelberg: Springer-Verlag, p. 149.Google Scholar
  7. 7.
    Nacozy, P.: Time Elements. Presented at Proc. Symp. on Satellite Dynamics. Berlin: Springer-Verlag, 1974.Google Scholar
  8. 8.
    Beaudet, P.: The Testing and Comparison of Various Methods of Special Perturbations. CSC 3000–08600–01TM, March 1974.Google Scholar
  9. 9.
    Baumgarte, J.; Stiefel, E.: Examples of Transformations Improving the Numerical Accuracy of the Integration of Differential Equations. Procedures of the Conference on the Numerical Solution of Ordinary Differential Equations, Springer-Verlag, p. 207.Google Scholar
  10. 10.
    Nacozy, P.: University of Texas at Austin, private communi cation.Google Scholar
  11. 11.
    Scheifele, G.: Numerical Orbit Computation Based on a Canonical Intermediate Orbit. Report for ESRO, ESOCContract 490/72/AR, September 1973.Google Scholar
  12. 12.
    Samway, R.: A Special Perturbation Method Based on Canonical Delaunay-Similar Elements with the True Anomaly as the Independent Variable. AMRL 1054, University of Texas at Austin, July 1973.Google Scholar
  13. 13.
    Penas, A.: Accurate Integration of Orbits Using Delaunay–Similar Elements. GSFC X–document 582–73–375, December 1973.Google Scholar

Copyright information

© Springer-Verlag, Berlin/Heidelberg 1975

Authors and Affiliations

  • C. E. Velez
    • 1
  1. 1.NASA/Goddard Space Flight CenterGreenbeltUSA

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