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Linear and Nonlinear Oscillators

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

Abstract

The linear oscillator is a simple model that lies at the foundation of many physical phenomena and plays a crucial role in accelerator dynamics. Many systems can be viewed as an approximation to a set of independent linear oscillators. In this chapter, we will review the main properties of the linear oscillator including its response to resonant excitations, slowly varying forces, random kicks, and parametric variation of the frequency. We will discuss the impact of damping terms as well as how small, nonlinear terms in the oscillator equation modify the oscillator frequency and lead to nonlinear resonance.

References

  1. 1.
    Wolfram Research, Inc. Mathematica, Version 11.2, 2017Google Scholar
  2. 2.
    L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics, 3rd edn., Mechanics (Elsevier Butterworth-Heinemann, Burlington MA, 1976). (translated from Russian)Google 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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