Abstract

The motion of a ship in long beam seas could be described by a second-order non-linear differential equation, having the roll angle as variable and depending on four parameters. With the direct forcing amplitude as bifurcation parameter, the dynamical system exhibits either periodic or chaotic behaviour, the route to chaos being realized by a period doubling sequence of periodic motions. Some accepted indicators, like bifurcation diagrams, phase planes and Poincare sections have been computed and they confirm the transition from order to chaos. In the main part of the paper, the harmonic balance method is used to obtain approximate solutions for the periodic motions and to predict the period doubling bifurcations by a stability analysis.