Skip to main content
SpringerLink
Log in

Extension and application of Newton's method in nonlinear oscillation theory

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

Abstract

In this paper we suggest and prove that Newton's method may calculate the asymptotic analytic periodic solution of strong and weak nonlinear nonautonomous systems, so that a new analytic method is offered for studying strong and weak nonlinear oscillation systems. On the strength of the need of our method, we discuss the existence and calculation of the periodic solution of the second order nonhomogeneous linear periodic system. Besides, we investigate the application of Newton's method to quasi-linear systems. The periodic solution of Duffing equation is calculated by means of our method.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Li Zheng-Yuan and Chien Min,The Rotation Degree Theory in Field of Vectors and Its Application, Pekjing University Press (1982). (in Chinese)

  2. Bogoliubov, N. N., and Y. A. Mitropolsky,Asymptotic Method in the Theory of Nonlinear Oscillation, Science Press (1974). (in Russian)

  3. Malkin, I. G.,Liapnov Method and Poincaré Method in the Theory of Nonlinear Oscillations, Science Press (1959). (Chinese version)

  4. Nayfeh and Mook,Nonlinear Oscillation, New York (1978).

  5. Xu Zhao, A new asymptotic method in nonlinear mechanics,Acta Mechanics Sinica,17, 3 (1985).

    Google Scholar 

  6. Li Li, The periodic solution of quasi-conservative system,Proceedings of the Int. Conf. on Nonl. Mech., Science Press (1985).

  7. Burton, T. D., Nonlinear oscillation limit cycle analysis using a time transformation approach,Int. J. Nonlinear Mech.,17, 1 (1982).

    Article  MathSciNet  Google Scholar 

  8. Contolovich, L. V., and G. P. Ackilov,Functional Analysis, Advanced Education Press (1984). (Chinese version)

  9. Ouyang Guang-zhong,Mathematical Analysis, Advanced Education Press (1985). (in Chinese)

  10. Lusjelnick, L. A., and G. P. Ackilov,Functional Analysis Bases, Science Press, Moscow (1965). (in Russian)

    Google Scholar 

  11. Lin Chien-bo,Nonlinear Oscillations in the Physical Systems, translated by Northeast Institute of Technology (1980).

Download references

Author information

Authors and Affiliations

  1. Tianjin University, Tianjin

    Huo Lin-chun

Authors
  1. Huo Lin-chun
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Li Li

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lin-chun, H. Extension and application of Newton's method in nonlinear oscillation theory. Appl Math Mech 13, 861–876 (1992). https://doi.org/10.1007/BF02481805

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02481805

Key words

Search

Navigation