IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v79y2008i2p149-166.html
   My bibliography  Save this article

Stability and bifurcation analysis for a model of a nonlinear coupled pitch–roll ship

Author

Listed:
  • Zhou, Liangqiang
  • Chen, Fangqi

Abstract

Using a combination of analytical and numerical methods, the paper studies the stability and bifurcations for a model of a nonlinear coupled pitch–roll ship. The model represents a two-degree-of-freedom system with quadratic coupling subjected to a modulated sinusoidal excitation. Three types of critical points for the bifurcation response equations near the combination resonance in the presence of internal resonance are considered. These points are characterized by a double zero and two negative eigenvalues, a double zero and a pair of purely imaginary eigenvalues, and two pairs of purely imaginary eigenvalues, respectively. For each case, the stability regions for the initial equilibrium solution and the critical bifurcation curves are obtained. The amplitude response curves with respect to detuning/damping parameters for critical bifurcation parameters are obtained for the first two types, and detailed analyses of the eigenvalues of the linearized system for each parametric region are given. For the third type, with the aid of normal form theory, the explicit expressions of the critical bifurcation curves leading to incipient and secondary bifurcations are obtained. Bifurcations leading to 2D, 3D tori and their stability conditions are also investigated. Some new dynamical behaviors are presented for this system.

Suggested Citation

  • Zhou, Liangqiang & Chen, Fangqi, 2008. "Stability and bifurcation analysis for a model of a nonlinear coupled pitch–roll ship," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(2), pages 149-166.
    • Handle: RePEc:eee:matcom:v:79:y:2008:i:2:p:149-166
    DOI: 10.1016/j.matcom.2007.11.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037847540700314X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2007.11.008?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. Kamel, M.M., 2007. "Bifurcation analysis of a nonlinear coupled pitch–roll ship," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(5), pages 300-308.
    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. Wenjie Zhang & Pin Wu & Yan Peng & Dongke Liu, 2019. "Roll Motion Prediction of Unmanned Surface Vehicle Based on Coupled CNN and LSTM," Future Internet, MDPI, vol. 11(11), pages 1-15, November.

    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.

      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:matcom:v:79:y:2008:i:2:p:149-166. 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/mathematics-and-computers-in-simulation/ .

      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.