Norrbin's nonlinear model

Norrbin’s nonlinear model extends the linear Nomoto steering equation by adding a cubic yaw-rate term, written T r_dot + r + alpha r^3 = K delta, where r is yaw rate, delta is rudder angle, K is the steering gain, T is the time constant, and alpha is the nonlinear coefficient. The alpha r^3 term captures the loss of effectiveness at large turning rates and, when the underlying spiral is unstable, reproduces the hysteresis loop a directionally unstable hull shows. It is widely used for course-keeping controller design and for fitting trial or simulation data, sitting between the linear Nomoto model and full Abkowitz hydrodynamic-derivative models.