Stability analysis of nonlinear ship-roll dynamics under wind and wave

Considering the nonlinear damping and restoring moments, a nonlinear ship rolling dynamical system is established in this paper. When only subjected to periodic wave excitation, the system is symmetric, whereas when subjected to joint action of periodic wave excitation and crosswind, the system degenerates into asymmetric. The simple zero points of Melnikov function in both two kinds of dynamical systems are computed by virtue of Gauss–Legendre integration. As a numerical verification of the threshold value, Lyapunov exponents are computed. In the end of the paper, the motion stability and the effect of crosswind on stability are analyzed by means of safe basin simulation and observation of its gradual erosion phenomenon. The study shows that crosswind results in symmetry breaking and further reduces the stability of the rolling system.