Nonlinear dynamics of ship oscillations

The stability of a ship´s motions is crucial for the safety of its crew, its cargo, and the environment. To prevent losses due to unstable motions, particularly in high seas, a better understanding of ship stability is necessary. We analyze the stability of ship motions using a hydrodynamic model accounting for all the rigid body motions of a ship, as well as memory effects in the fluid. The analysis of a particular ship shows that ship´s dynamics depend strongly on the nonlinearities of the ship-fluid-system. Before the ship capsizes we notice a bifurcation when wave heights increase. A path following method is employed to determine in a systematic manner the stability limits. The application for a simplified system shows the importance of the nonlinearities of the mathematical model