Skip to main content
SpringerLink
Log in

Perturbation method in the theory of nonlinear oscillations

  • Published:
Celestial mechanics Aims and scope Submit manuscript

Abstract

Asymptotic recurrence formulas for treating nonlinear oscillation problems are presented. These formulas are based on a Lie transform similar to that described by Deprit for Hamiltonian systems. It is shown that the basic formulas have essentially the same forms as those obtained by Deprit and by the present author in the Hamiltonian case.

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

  • Bogoliubov, N. N. and Mitropolsky, Y. A.: 1961,Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York.

    Google Scholar 

  • Deprit, A.: 1969,Celestial Mech. 1, 12–30.

    Google Scholar 

  • Deprit, A. and Rom, A. R. M.: 1967,Z. angew. Math. Physik 18, 736–747.

    Google Scholar 

  • Henrard, J.: 1970, ‘On a Perturbation Theory Using Lie Transforms’Celestial Mech. 3, 107–120.

    Google Scholar 

  • Kamel, A. A.: 1969,Celestial Mech. 1, 190–199.

    Google Scholar 

  • Kevorkian, J.: 1966, ‘Space Mathematics’,Am. Math. Soc., 206–275.

  • Morrison, J. A.: 1966,Progress in Aeronautics, Vol. 17, Academic Press, New York, pp. 117–138.

    Google Scholar 

  • Musen, P.: 1965,J. Astronaut. Sci. 12, 129–134.

    Google Scholar 

  • Nayfeh, A. H.: 1965,Math. Phys. 44, 364–374.

    Google Scholar 

  • Poincaré, H.: 1957,Les méthodes nouvelles de la mécanique céleste Vol. III, Dover Publications, New York.

    Google Scholar 

  • Sandri, G.: 1963,Ann. Phys. 24, 332–379.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Aeronautics and Astronautics, Stanford University, Stanford, Calif., U.S.A.

    Ahmed Aly Kamel

Authors
  1. Ahmed Aly Kamel
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aly Kamel, A. Perturbation method in the theory of nonlinear oscillations. Celestial Mechanics 3, 90–106 (1970). https://doi.org/10.1007/BF01230435

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01230435

Keywords

Search

Navigation