The turning of vessels using bow and stern thrusters, particularly in restricted waters, is of much operational concern. In this paper, the equation of motion has been set up precisely and two approaches to finding solutions to it are presented. The first approach is without mathematical approximation and can only be solved partially; further progress means resorting to numerical or graphical methods. The second approach examines some particular situations where approximate analytical techniques might be exploited. The results from this latter approach give indications as to how coefficients, appearing in the dynamic equation, might be established from some simple tests.
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