Nonlinear dynamics of close proximity ship towing

Abstract

The goal of this study is to investigate the nonlinear dynamics of two ships in close proximity towing. The sway and yaw dynamics of both the leading and the trailing ships were included in the formulation. Previous studies were restricted to a linear analysis, which can accurately predict the regions of stability and instability for the system. The mechanism of loss of stability can be assessed with a systematic nonlinear analysis. The analysis is based on Taylor series expansions of the equations of motion up to third order terms. It is shown that the primary loss of stability occurs in the form of Hopf bifurcations to periodic solutions. A nonlinear stability coefficient was calculated which allows characterization of the stability properties of the resulting limit cycles. The results indicate the effects of ship separation and towing tension on motion stability.