IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v242y1997i1p239-249.html
   My bibliography  Save this article

Stability regions for coupled Hill's equations

Author

Listed:
  • Mahmoud, Gamal M.

Abstract

In this paper we extend well-known results for one Hill's equation and present the stability analysis of two coupled Hill's equations for which the general theory is not readily available. Approximate expressions are derived in the context of peturbation theory for the boundaries between bounded and unbounded periodic solutions with frequencies ω = n/m (n and m are positive integers) of both linear and nonlinear coupled Mathieu equations as examples. Excellent agreement is found between theoretical predictions and numerical computations over large ranges of parameter values and initial conditions. These periodic solutions are important because they correspond to some of the lowest-order resonances of the system and when they are stable, they turn out to have large regions of regular motion around them in phase space. Coupled Mathieu equations appear in numerous important physical applications, in problems of accelerator dynamics, electrohydrodynamics and mechanics.

Suggested Citation

  • Mahmoud, Gamal M., 1997. "Stability regions for coupled Hill's equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 242(1), pages 239-249.
    • Handle: RePEc:eee:phsmap:v:242:y:1997:i:1:p:239-249
    DOI: 10.1016/S0378-4371(97)00194-5
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437197001945
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/S0378-4371(97)00194-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xu, Yong & Xu, Wei & Mahmoud, Gamal M. & Lei, Youming, 2005. "Beam–beam interaction models under narrow-band random excitation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(3), pages 372-386.
    2. Mahmoud, Gamal M. & Bountis, Tassos & Ahmed, Sayed A., 2000. "Stability analysis for systems of nonlinear Hill's equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 286(1), pages 133-146.
    3. Mahmoud, Gamal M. & Aly, Shaban A.H., 2000. "On periodic solutions of parametrically excited complex non-linear dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(3), pages 390-404.
    4. Xu, Yong & Xu, Wei & Mahmoud, Gamal M, 2004. "On a complex beam–beam interaction model with random forcing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 347-360.
    5. Cveticanin, L., 2001. "Analytic approach for the solution of the complex-valued strong non-linear differential equation of Duffing type," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 297(3), pages 348-360.
    6. Xu, Yong & Zhang, Huiqing & Xu, Wei, 2007. "On stochastic complex beam–beam interaction models with Gaussian colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 259-272.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:242:y:1997:i:1:p:239-249. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.