Skip to main content
Log in

Elapsed time of periodic motion with negative damping

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

Abstract

An initially periodic motion is gradually raised out of the potential well by the effect of negative damping. The elapsed time when the motion ceases to be periodic is obtained by multiple variable expansions. An example of a strictly nonlinear system shows, the result has a good approximation and is easy to calculate.

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

Access this article

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. Li Y. P. and J. Kevorkian, The effects of wiggler taper rate and signal, field gain rate in free-electron lasers,IEEE J. Quantum Electron,24 (1988), 598–608.

    Article  Google Scholar 

  2. Kuzmak, G. E., Asymptotic solutions of nonlinear second order differential equations with variable coefficeints,P. M. M.,23 (1959), 515–526.

    MATH  MathSciNet  Google Scholar 

  3. Luke, J. C., A perturbation method for nonlinear dispersive wave problems,Proc. Roy. Soc., Ser. A,292 (1966), 403–412.

    MATH  MathSciNet  Google Scholar 

  4. Dai Shi-qiang and Zhuang Feng-qing, Asymptotic solutions for a class of nonlinear oscillation systems,Scientia Sinia (Series A),29 (1986) 737–744.

    Google Scholar 

  5. Li, Y. P., Free electron lasers with variable parameter wigglers, a strictly nonlinear oscillator with slowly varying paramaters Ph. D. dissertation, Univ. of Wash. Seattle, WA (1987), Dept. Appl Math., UW, Tech. Rep. 87-2 (1987).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by Li Li

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yi-ping, L. Elapsed time of periodic motion with negative damping. Appl Math Mech 13, 719–723 (1992). https://doi.org/10.1007/BF02451537

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02451537

Key words

Navigation