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Classical Planar Scattering by Coulombic Potentials

  • Markus Klein
  • Andreas Knauf

Part of the Lecture Notes in Physics Monographs book series (LNPMGR, volume 13)

Table of contents

  1. Front Matter
    Pages i-v
  2. Pages 1-9
  3. Pages 23-33
  4. Pages 35-39
  5. Pages 55-72
  6. Pages 73-80
  7. Pages 89-93
  8. Pages 95-103
  9. Pages 129-133
  10. Back Matter
    Pages 135-142

About this book

Introduction

Astronomy as well as molecular physics describe non-relativistic motion by an interaction of the same form: By Newton's respectively by Coulomb's potential. But whereas the fundamental laws of motion thus have a simple form, the n-body problem withstood (for n > 2) all attempts of an explicit solution. Indeed, the studies of Poincare at the end of the last century lead to the conclusion that such an explicit solution should be impossible. Poincare himselfopened a new epoch for rational mechanics by asking qual­ itative questions like the one about the stability of the solar system. To a largeextent, his work, which was critical for the formation of differential geometry and topology, was motivated by problems arising in the analysis of the n-body problem ([38], p. 183). As it turned out, even by confining oneselfto questions ofqualitativenature, the general n-body problem could not be solved. Rather, simplified models were treated, like planar motion or the restricted 3-body problem, where the motion of a test particle did not influence the other two bodies.

Keywords

Chaotic Scattering Chaotische Streuung Coulomb-artige Singularitäten Coulombic Singularity Differentialgeometrie Dynamische Systeme Ergodentheorie Ergodic Theory differential geometry dynamical systems

Authors and affiliations

  • Markus Klein
    • 1
  • Andreas Knauf
    • 1
  1. 1.Technische UniversitätBerlin 12Germany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-47336-7
  • Copyright Information Springer Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-55987-0
  • Online ISBN 978-3-540-47336-7
  • Series Print ISSN 0940-7677
  • Buy this book on publisher's site
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