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The Global Phase Structure of the Three Dimensional Isosceles Three Body Problem with Zero Energy

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Hamiltonian Dynamical Systems

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 63))

Abstract

We study the global flow defined by the three-dimensional isosceles three-body problem with zero energy. A new set of coordinates and a scaled time are introduced which alow the phase space to be compactified by adding boundary manifolds. Geometric argument gives an almost complete sketch of the global phase portrait of this gravitational system.

Institute for Dynamics, Department of Mathematics, University of Cincinnati, Cincinnati, Ohio 45221-0025. This research partially supported by grants from the National Science Foundation.

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References

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Author information

Authors and Affiliations

  1. Institute for Dynamics, Department of Mathematics, University of Cincinnati, Cincinnati, Ohio, 45221-0025, USA

    Kenneth R. Meyer

  2. Institute for Dynamics, Department of Mathematics, University of Cincinnati, Cincinnati, Ohio, 45221-0025, USA

    Quidong Wang

Authors
  1. Kenneth R. Meyer
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  2. Quidong Wang
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Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, University of Cincinnati, 45221, Cincinnati, OH, USA

    H. S. Dumas

  2. Institute for Dynamics Department of Mathematical Sciences, University of Cincinnati, 45221, Cincinnati, OH, USA

    K. S. Meyer

  3. Department of Computer Science, University of Cincinnati, 45221, Cincinnati, OH, USA

    D. S. Schmidt

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© 1995 Springer-Verlag New York, Inc.

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Meyer, K.R., Wang, Q. (1995). The Global Phase Structure of the Three Dimensional Isosceles Three Body Problem with Zero Energy. In: Dumas, H.S., Meyer, K.S., Schmidt, D.S. (eds) Hamiltonian Dynamical Systems. The IMA Volumes in Mathematics and its Applications, vol 63. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8448-9_18

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  • DOI: https://doi.org/10.1007/978-1-4613-8448-9_18

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8450-2

  • Online ISBN: 978-1-4613-8448-9

  • eBook Packages: Springer Book Archive

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