IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v27y2006i5p1220-1228.html
   My bibliography  Save this article

Oscillators in resonance p:q:r

Author

Listed:
  • Arribas, M.
  • Elipe, A.
  • Floría, L.
  • Riaguas, A.

Abstract

A canonical transformation is proposed to handle Hamiltonian systems made of the addition or subtraction of three harmonic oscillators in p:q:r resonance. This transformation is an extension of the classical Lissajous transformation for the 1:1 resonance. Our extended Lissajous variables consist of three pairs of action-angle variables, which makes possible the application of perturbation theories without encountering small divisors. A set of functions, related with the Lissajous variables, are found, and are used to describe the phase flow of reduced space after normalization.

Suggested Citation

  • Arribas, M. & Elipe, A. & Floría, L. & Riaguas, A., 2006. "Oscillators in resonance p:q:r," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1220-1228.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:5:p:1220-1228
    DOI: 10.1016/j.chaos.2005.04.085
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905004352
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.04.085?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. de Bustos, María T. & Guirao, Juan L.G. & Llibre, Jaume & Vera, Juan A., 2016. "New families of periodic orbits for a galactic potential," Chaos, Solitons & Fractals, Elsevier, vol. 82(C), pages 97-102.
    2. Llibre, Jaume & Paşca, Daniel & Valls, Claudià, 2014. "Periodic solutions of a galactic potential," Chaos, Solitons & Fractals, Elsevier, vol. 61(C), pages 38-43.

    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:chsofr:v:27:y:2006:i:5:p:1220-1228. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.