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

Liangqiang Zhou and Fangqi Chen

Mathematics and Computers in Simulation (MATCOM), 2008, vol. 79, issue 2, 149-166

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.

Keywords: Nonlinear coupled pitch–roll ship model; Bifurcation; Stability; Normal form (search for similar items in EconPapers)
Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S037847540700314X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2008:i:2:p:149-166

DOI: 10.1016/j.matcom.2007.11.008

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().