IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v247y1997i1p281-311.html
   My bibliography  Save this article

Mode competition in a system of two parametrically driven pendulums; the role of symmetry

Author

Listed:
  • Banning, E.J.
  • van der Weele, J.P.
  • Kettenis, M.M.

Abstract

This paper is the final part in a series of four on the dynamics of two coupled, parametrically driven pendulums. In the previous three parts (Banning and van der Weele, Mode competition in a system of two parametrically driven pendulums; the Hamiltonian case, Physica A 220 (1995) 485–533; Banning et al., Mode competition in a system of two parametrically driven pendulums; the dissipative case, Physica A 245 (1997) 11–48; Banning et al., Mode competition in a system of two parametrically driven pendulums with nonlinear coupling, Physica A 245 (1997) 49–98) we have given a detailed survey of the different oscillations in the system, with particular emphasis on mode interaction. In the present paper we use group theory to highlight the role of symmetry. It is shown how certain symmetries can obstruct period doubling and Hopf bifurcations; the associated routes to chaos cannot proceed until these symmetries have been broken. The symmetry approach also reveals the general mechanism of mode interaction and enables a useful comparison with other systems.

Suggested Citation

  • Banning, E.J. & van der Weele, J.P. & Kettenis, M.M., 1997. "Mode competition in a system of two parametrically driven pendulums; the role of symmetry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 247(1), pages 281-311.
    • Handle: RePEc:eee:phsmap:v:247:y:1997:i:1:p:281-311
    DOI: 10.1016/S0378-4371(97)00388-9
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437197003889
    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)00388-9?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.

    References listed on IDEAS

    as
    1. Schaeffer, Peter V., 1988. "Family migration in an uncertain environment," Socio-Economic Planning Sciences, Elsevier, vol. 22(5), pages 221-227.
    2. Haase, Knut, 1994. "Capacitated lot-sizing with sequence dependent setup costs," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 340, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    3. Banning, E.J. & van der Weele, J.P. & Ross, J.C. & Kettenis, M.M. & de Kleine, E., 1997. "Mode competition in a system of two parametrically driven pendulums; the dissipative case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(1), pages 11-48.
    4. Banning, E.J & van der Weele, J.P, 1995. "Mode competition in a system of two parametrically driven pendulums; the Hamiltonian case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 220(3), pages 485-533.
    5. Banning, E.J. & van der Weele, J.P. & Ross, J.C. & Kettenis, M.M., 1997. "Mode competition in a system of two parametrically driven pendulums with nonlinear coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(1), pages 49-98.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Banning, E.J. & van der Weele, J.P. & Ross, J.C. & Kettenis, M.M. & de Kleine, E., 1997. "Mode competition in a system of two parametrically driven pendulums; the dissipative case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(1), pages 11-48.
    2. Banning, E.J. & van der Weele, J.P. & Ross, J.C. & Kettenis, M.M., 1997. "Mode competition in a system of two parametrically driven pendulums with nonlinear coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(1), pages 49-98.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Banning, E.J. & van der Weele, J.P. & Ross, J.C. & Kettenis, M.M., 1997. "Mode competition in a system of two parametrically driven pendulums with nonlinear coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(1), pages 49-98.
    2. Banning, E.J. & van der Weele, J.P. & Ross, J.C. & Kettenis, M.M. & de Kleine, E., 1997. "Mode competition in a system of two parametrically driven pendulums; the dissipative case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(1), pages 11-48.
    3. Drexl, Andreas & Haase, Knut, 1995. "Proportional lotsizing and scheduling," International Journal of Production Economics, Elsevier, vol. 40(1), pages 73-87, June.
    4. Haase, Knut & Göpfert, Lars, 1995. "Engpaßorientierte Fertigungssteuerung bei reihenfolgeabhängigen Rüstvorgängen in einem Unternehmen der Satz- und Drucktechnik," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 373, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.

    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:247:y:1997:i:1:p:281-311. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.