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The Birkhoff and B 3 Regularizing Transformations

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Singularities in Gravitational Systems

Part of the book series: Lecture Notes in Physics ((LNP,volume 590))

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Abstract

The Birkhoff transformation for the restricted circular planar three body problem is introduced using a Hamiltonian formalism. A generalization of the Birkhoff transformation (hereafter the B 3 transformation) is derived in order to regularize the circular spatial three body problem by means of a geometrical approach. These transformations have the important property to provide a simoultaneous regularization of two singularities.

Some results about numerical integrations before and after the regularization are presented.

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References

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Author information

Authors and Affiliations

  1. Observatoire de Nice, B.P.4229, F-06304, Nice Cedex 4, France

    Maria Gabriella & Della Penna

Authors
  1. Maria Gabriella
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  2. Della Penna
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Editor information

Editors and Affiliations

  1. O.C.A. Observatoire de Nice, B.P. 4229, 06304, Nice Cedex 4, France

    Daniel Benest  & Claude Froeschlé  & 

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© 2002 Springer-Verlag Berlin Heidelberg

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Gabriella, M., Penna, D. (2002). The Birkhoff and B 3 Regularizing Transformations. In: Benest, D., Froeschlé, C. (eds) Singularities in Gravitational Systems. Lecture Notes in Physics, vol 590. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48009-9_3

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  • DOI: https://doi.org/10.1007/3-540-48009-9_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43765-9

  • Online ISBN: 978-3-540-48009-9

  • eBook Packages: Springer Book Archive

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