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Stabilization by modification of the Lagrangian

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Abstract

In order to reduce the error growth during a numerical integration, a method of stabilization, of the differential equations of the Keplerian motion is offered. It is characterized by the use of the eccentric anomaly as independent variable in such a way that the time transformation is given by a generalized Lagrange formalism. The control terms in the equations of motion obtained by this modified Lagrangian give immediately a completely Lyapunov-stable set of differential equations. In contrast to other publications, here the equation of time integration is modified by a control term which leads to an integral which defined the time element for the perturbed Keplerian motion.

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References

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Authors and Affiliations

  1. Mechanik-Zentrum, Technische Universitat Braunschweig, Federal Republic of Germany

    Joachim W. Baumgarte

  2. Swiss Federal Institute of Technology, Zürich, Switzerland

    Joachim W. Baumgarte

Authors
  1. Joachim W. Baumgarte
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Additional information

This paper was supported by the National Research Council and the National Aeronautics and Space Administration and also by the Deutsche Forschungsgemeinschaft. It was presented at the Flight Mechanics/Estimation Theory Symposium, Goddard Space Flight Center, Greenbelt, Md., April 15–16, 1975.

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Baumgarte, J.W. Stabilization by modification of the Lagrangian. Celestial Mechanics 13, 247–251 (1976). https://doi.org/10.1007/BF01232727

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  • DOI: https://doi.org/10.1007/BF01232727

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