Skip to main content
SpringerLink
Log in

Periodic solution and chaotic behavior of a class of nonautonomic pendulum systems with large damping

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

In this paper the existence and uniqueness of the periodic solution is studied for a class of second order nonautonomic pendulum systems

$$\bar x + a\dot x + \varphi (t)\sin x = F(t)$$

and the parameter regions for which the system in chaos is investigated when

$$\varphi (t) = 1 - \varepsilon \lambda \cos \omega t, F(t) = \beta + \varepsilon \mu (\cos \omega t - \omega \sin \omega t)$$

and the damping coefficient a>0 is large. The results obtained generalize the corresponding conclusions of papers [1–8].

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Sun Jian-hua, Chaotic motions of the pendulum systems.J. Nanjing University, Math. Biquarterly,4, 1 (1987), 43–50. (in chinese)

    Google Scholar 

  2. Qían Min, et al., Theoretic analysis of I–V characteristics in Josephson junction.Acta Physica Sinica,36, 2 (1987), 149–156. (in Chinese)

    Google Scholar 

  3. Wang Rong-liang, Research of a P-L-L with sine characteristic and frequency modulation.J. Engin. Math.,3, 2 (1986), 142–144. (in Chinese)

    Google Scholar 

  4. Sansone, G. and R. Conti,Nonlinear Differential Equation. Pergamon Press (1964).

  5. Beasley, M.R. and B.A. Huberman, Chaos in Josephson junctions.Comm. Sol. Sta. Phys.,10 (1982), 155–162.

    Google Scholar 

  6. Ben-Jacob, E., et al., Intermittent chaos in Josephson junctions,Phys. Rev. Lett.,49 (1982), 1599–1602.

    Google Scholar 

  7. Cirillo, M. and N.F. Pederson, On bifurcations and transition to chaos in a Josephson junctions,Phys. Lett. 90A (1982), 150–152.

    Google Scholar 

  8. Guckenheimer, J. and P. Holmes,Nonlinear Oscillations. Dynamical Systems and Bifurcations of Vector Fields. Springer-Verlag (1983).

  9. Lasalle, J.I., and S. Lefschetz,Stability by Lyapunov's Direct Method with Application. New York, Academic Press (1961).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Nanjing University, Nanjing

    Sun Jian-hua

Authors
  1. Sun Jian-hua
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Su Yu-cheng

Supported by Science Fundation of Young Teachers of Nanjing University.

Finally, I would like lo thank my teacher. professor Luo Ding-jun for his help.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jian-hua, S. Periodic solution and chaotic behavior of a class of nonautonomic pendulum systems with large damping. Appl Math Mech 9, 1195–1204 (1988). https://doi.org/10.1007/BF02014474

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02014474

Keywords

Search

Navigation