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The Three-Body Problem

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Part of the Grundlehren der mathematischen Wissenschaften book series (volume 187)

Abstract

Ours, according to Leibniz, is the best of all possible worlds, and the laws of nature can therefore be described in terms of extremal principles. Thus, arising from corresponding variational problems, the differential equations of mechanics have invariance properties relative to certain groups of coordinate transformations. Because this is particularly important for celestial mechanics, in the preliminary sections we will develop as much of the transformation theory for the Euler-Lagrange and the Hamiltonian equations as is desirable for our purposes.

Keywords

  • Canonical Transformation
  • Short Side
  • Jacobian Determinant
  • Convergent Power Series
  • Mass Integral

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: 10.1007/978-3-642-87284-6_1
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© 1995 Springer-Verlag Berlin Heidelberg

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Siegel, C.L., Moser, J.K. (1995). The Three-Body Problem. In: Lectures on Celestial Mechanics. Grundlehren der mathematischen Wissenschaften, vol 187. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-87284-6_1

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  • DOI: https://doi.org/10.1007/978-3-642-87284-6_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58656-2

  • Online ISBN: 978-3-642-87284-6

  • eBook Packages: Springer Book Archive