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Canonical orbital elements in terms of an arbitrary independent variable

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Abstract

Within the framework of the Hamiltonian mechanics in the extended phase space, a set of canonical elements of the Delaunay type is developed in terms of an arbitrary independent angular variable. Application to the four classical anomalies-eccentric, true, elliptic, and mean-is presented. Particular attention is given to the generalized time equation and its conjugate energy equation.

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References

  • Baumgarte, J.: 1972,Celes. Mech. 5, 490.

    Google Scholar 

  • Bond, V. R.: 1976,Celes. Mech. 13, 287.

    Google Scholar 

  • Bond, V. R. and Broucke, R.: 1979,Celes. Mech. 21, 357.

    Google Scholar 

  • Brouwer, D. and Clemence, G. M.: 1961,Methods of Celestial Mechanics, Academic Press.

  • Graf, O. F. and Mueller, A. C.: 1979, ‘A study of the Lifetime of Geosynchronous Transfer Orbits’, AIAA Paper No. 79-105.

  • Hamilton, W. R.: 1834, ‘On a General Method in Dynamics and Second Essay on a General Method in Dynamics’,Hamilton's Collected Papers, Cambridge University Press (1940).

  • Janin, G. and Bond, V. R.: 1980, ‘The Elliptic Anomaly’, NASA TM 58228.

  • Mueller, A., Scheifele, G. and Starke, S.: 1979, ‘An Analytical Orbit Predictor for Near-Earth Satellites’, AIAA Paper No. 79-122.

  • Nacozy, P. E.: 1977,Celes. Mech. 16, 309.

    Google Scholar 

  • Santilli, R. M.: 1978,Foundations of Theoretical Mechanics I. The Inverse Problem in Newtonian Mechanics, Springer Verlag, New York, Heidelberg, Berlin.

    Google Scholar 

  • Scheifele, G.: 1970,Celes. Mech. 2, 296–310.

    Google Scholar 

  • Scheifele, G. and Graf, O.: 1974, ‘Analytical Satellite Theory Based on a New Set of Canonical Elements’, AIAA Paper No. 74-838.

  • Stiefel, E. and Scheifele, G.: 1971,Linear and Regular Celestial Mechanics, Springer Verlag, New York, Heidelberg, Berlin.

    Google Scholar 

  • Szebehely, V.: 1967,Theory of Orbits, Academic Press.

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Author notes

  1. Guy Janin

    Present address: European Space Operations Center, Darmstadt, Federal Republic of Germany

Authors and Affiliations

  1. National Aeronautics and Space Administration, Lyndon B. Johnson Space Center, Houston, Texas, USA

    Victor R. Bond & Guy Janin

Authors
  1. Victor R. Bond
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  2. Guy Janin
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Bond, V.R., Janin, G. Canonical orbital elements in terms of an arbitrary independent variable. Celestial Mechanics 23, 159–172 (1981). https://doi.org/10.1007/BF01229551

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  • DOI: https://doi.org/10.1007/BF01229551

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