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Averaging and Normalization in Celestial Mechanics

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Part of the Astrophysics and Space Science Library book series (ASSL,volume 441)

Abstract

In this Chapter, the basic concepts of the perturbation approach (needed to present the Lidov-Kozai theory and its modern advances) are considered.

Keywords

  • Deprit Hori Method
  • Delaunay Variables
  • Birkhoff Normal Form
  • Normalizing Transformation
  • Keplerian Orbital Elements

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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  • DOI: 10.1007/978-3-319-43522-0_2
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Notes

  1. 1.

    The three bodies are called the primary, the secondary, and the tertiary in accord (usually) with the hierarchy of their masses. However, other ways of enumeration are also possible, e.g., according to the hierarchy of the geometric configuration. This is usually clear from the context. The two “primaries” comprise the primary and the secondary.

  2. 2.

    Note that in this book all vector quantities are set in bold font.

  3. 3.

    Approximating the orbital motion of a body at a given instant in a best way (in some sense; see, e.g., Murray and Dermott 1999).

  4. 4.

    The method was originally introduced by Poincaré (1899).

References

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Shevchenko, I.I. (2017). Averaging and Normalization in Celestial Mechanics. In: The Lidov-Kozai Effect - Applications in Exoplanet Research and Dynamical Astronomy. Astrophysics and Space Science Library, vol 441. Springer, Cham. https://doi.org/10.1007/978-3-319-43522-0_2

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