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Action-Angle Variables and Liouville’s Theorem

  • Gennady StupakovEmail author
  • Gregory Penn
Chapter
Part of the Graduate Texts in Physics book series (GTP)

Abstract

One of the most powerful uses of canonical transformations is to express the dynamics in terms of action-angle variables. These are phase space coordinates which provide a simple description of the Hamiltonian motion, and are widely used in particle dynamics. A geometrical view of the Hamiltonian flow in phase space leads us to the formulation of Liouville’s theorem that is crucial for understanding the fundamental properties of large ensembles of beam particles in accelerators.

References

  1. 1.
    E. Minguzzi, Rayleigh’s dissipation function at work. Eur. J. Phys. 36, 035014 (2016)CrossRefGoogle Scholar
  2. 2.
    J.H. Hubbard, B.B. Hubbard, Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, 2nd edn. (Prentice Hall, Upper Saddle River, 2001)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.SLAC National Accelerator LaboratoryStanford UniversityMenlo ParkUSA
  2. 2.Lawrence Berkeley National LaboratoryBerkeleyUSA

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