Nonlinear Stability Analysis of Ship Towed by Elastic Rope

The course stability of a towed vessel is traditionally assessed using local linear analysis of a time-independent system of a ship towed by an inelastic towline. In this work a method is developed for studying the global stability of a nonlinear time-dependent model of the horizontal plane motions of a ship towed by a nonlinear elastic rope. First, the critical points of the corresponding autonomous system are found in the phase space and their nature is determined by local analysis. Then the global behavior of the trajectories in the phase space is predicted on the basis of the local analysis results. The results of the stability analysis are verified by comparison with the solution of the model by simulation. A barge, a tanker and a Mariner, with markedly different course stability characteristics, towed by two different elastic ropes are used to illustrate the method.