Numerical study of some properties of generic mathematical models of directionally unstable ships

Dynamic properties of directionally unstable surface displacement ships in manoeuvring motion are studied on the basis of simplified nonlinear mathematical models by means of numerical simulation. First-order and second-order Nomoto equations are written in normalized form to minimize the number of the defining parameters. A piecewise-linear approximation is used for the static characteristic which is supposed to be fully defined by the hysteresis loop's height and width. The numerical simulations were carried out for the open-loop system under sinusoidal excitation and for the closed-loop system imitating the ship in zigzag manoeuvres. Somewhat anomalous responses were discovered when the rudder deflection amplitude is close to the loop's half-width.