The Journal of the Astronautical Sciences

, Volume 58, Issue 2, pp 153–165 | Cite as

Earth Satellite Perturbation Theories as Approximate KAM Tori

  • William E. Wiesel


Several standard Earth satellite general perturbation models can be converted into KAM tori, and are compared to KAM tori constructed from full geopotential integrations. Converting perturbation theories into tori allows absolute identification of spectral lines with the classical orbital elements. Comparisons are made of each torus representation against numerical integrations, and the torus spectra are also compared. The torus canonical coordinates Q i , are identified as the analogues of the “mean” mean anomaly\(\bar M\) , the longitude of the mean node\(\bar \Omega - {\theta _g}\), and the mean argument of perigee\(\bar \omega \). The associated torus canonical momenta P i are approximately the usual Delaunay momenta. A norm on multiply-periodic functions allows the actual “distance” between perturbation theory tori and actual geopotential tori to be measured, and the frequency errors can be estimated. KAM tori and numerical integration can agree to meter level accuracy over time intervals of a decade.


Earth Satellite Absolute Identification Earth Satellite Orbit Greenwich Meridian Keplerian Ellipse 
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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Copyright information

© American Astronautical Society, Inc. 2011

Authors and Affiliations

  • William E. Wiesel
    • 1
  1. 1.Department of Aeronautics and AstronauticsAir Force Institute of TechnologyWright-Patterson AFBUSA

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