Advertisement

Forced Pendulum

  • Leonid I. ManevitchEmail author
  • Agnessa Kovaleva
  • Valeri Smirnov
  • Yuli Starosvetsky
Chapter
Part of the Foundations of Engineering Mechanics book series (FOUNDATIONS)

Abstract

Harmonically forced pendulum is one of the basic models of nonlinear dynamics which has numerous applications in different fields of physics and mechanics. There are two main directions in the study of this model. First of them can be denoted as application of general mathematical perturbation theory in which integrable conservative system is a generating model.

References

  1. Arnold, V.I., Kozlov, V.V., Neishtadt, A.I.: Mathematical Aspects of Classical and Celestial Mechanics, 3rd ed. Encyclopaedia of Mathematical Sciences, vol. 3. Springer, Berlin (2006)Google Scholar
  2. Baker, G.I., Blackburn, J.A.: The Pendulum. A Case Study in Physics. Oxford University Press, New York (2005)zbMATHGoogle Scholar
  3. Bogoliubov, N.N., Mitropolskii, Y.A.: Asymptotic Methods in the Theory of Nonlinear Oscillations. Gordon and Breach, New York (1961)Google Scholar
  4. Chirikov, B.V., Zaslavsky, G.M.: Stochastic instability of nonlinear oscillations. Sov. Phys. Uspekhi 14, 549 (1972)CrossRefzbMATHGoogle Scholar
  5. Hale, J.K.: Oscillations in Nonlinear Systems. McGraw-Hill, New York (1963)zbMATHGoogle Scholar
  6. Manevitch, A.I., Manevitch, L.I.: The Mechanics of Nonlinear Systems with Internal Resonances. Imperial College Press, London (2005)CrossRefzbMATHGoogle Scholar
  7. Manevitch, L.I., Musienko, A.I.: Limiting phase trajectories and energy exchange between anharmonic oscillator and external force. Nonlinear Dyn. 58, 633 (2009)CrossRefzbMATHGoogle Scholar
  8. Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley-VCH Verlag GmbH and Co., Germany (2004)Google Scholar
  9. Neishtadt, A.I.: Passage through a separatrix in a resonance problem with a slowly-varying parameter. J. Appl. Math. Mech. 39(4), 594 (1975)MathSciNetCrossRefGoogle Scholar
  10. Neishtadt, A.I., Vasiliev, A.A.: Capture into resonance in dynamics of a classical hydrogen atom in an oscillating electric field. Phys. Rev. E 71, 056623 (2005)CrossRefGoogle Scholar
  11. Sagdeev, R.Z., Usikov, D.A., Zaslavsky, G.M.: Nonlinear Physics: From the Pendulum to Turbulence and Chaos. Harwood Academic Publishers, New York (1988)Google Scholar
  12. Scott, A.: Nonlinear Sciense: Emergence and Dynamics of Coherent Sructures. Oxford University Press, New York (2003)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Leonid I. Manevitch
    • 1
    Email author
  • Agnessa Kovaleva
    • 2
  • Valeri Smirnov
    • 1
  • Yuli Starosvetsky
    • 3
  1. 1.Institute of Chemical PhysicsRussian Academy of ScienceMoscowRussia
  2. 2.Space Research InstituteRussian Academy of ScienceMoscowRussia
  3. 3.Technion—Israel Institute of TechnologyFaculty of Mechanical EngineeringHaifaIsrael

Personalised recommendations