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Harmonic Balance Method and Stability of Discontinuous Systems

  • E. V. Kudryashova
  • N. V. KuznetsovEmail author
  • O. A. Kuznetsova
  • G. A. Leonov
  • R. N. Mokaev
Chapter

Abstract

The development of the theory of discontinuous dynamical systems and differential inclusions was not only due to research in the field of abstract mathematics but also a result of studies of particular problems in mechanics. One of the first methods, used for the analysis of dynamics in discontinuous mechanical systems, was the harmonic balance method developed in the thirties of the twentieth century. In our work, the results of analysis obtained by the method of harmonic balance, which is an approximate method, are compared with the results obtained by rigorous mathematical methods and numerical simulation.

Notes

Acknowledgement

This work was supported by the grant NSh-2858.2018.1 of the President of Russian Federation for the Leading Scientific Schools of Russia (2018–2019).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • E. V. Kudryashova
    • 1
  • N. V. Kuznetsov
    • 1
    • 2
    • 3
    Email author
  • O. A. Kuznetsova
    • 1
  • G. A. Leonov
    • 1
    • 4
  • R. N. Mokaev
    • 1
    • 5
  1. 1.Saint-Petersburg State UniversitySaint-PetersburgRussia
  2. 2.University of JyväskyläJyväskyläFinland
  3. 3.Institute of Problems of Mechanical Engineering RASSaint-PetersburgRussia
  4. 4.Institute of Problems of Mechanical Engineering RASSaint-PetersburgRussia
  5. 5.University of JyväskyläJyväskyläFinland

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