Further analysis of thruster-turning of ships at zero forward-speed; a time-domain approach

摘要

This Contribution is a sequel to that of the author's earlier paper, where the basic nonlinear equation of motion of a vessel turning, without forward speed, under the influence of water-resistance, wind-induced torque and thruster-torque was examined. The method of approach was to transform the basic dynamical equation, relating the angular position to time, into one relating angular velocity to angular position. In this paper, a time-domain solution is sought. However, the wind-induced torque is neglected in this analysis; this enables a number of special cases to be investigated that, as in the earlier paper, suggest simple trials whose results may enable some of the coefficients in the governing non-linear differential equation to be estimated. Further, the differential equation, governing the motion, is recognised to be of the Riccati type; this opens up the analysis to more complex thruster-torque profiles, for example, profiles having the mathematical form of polynomials in the time variable are examined.