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Aspects of de Wit's Equations Governing the Apparent Spontaneous Yaw of a Ship

de Wit has produced an analysis of the apparent spontaneous yaw of a ship when undergoing combined rolling and pitching. This analysis produces a set of four first-order simultaneous differential equations which govern the motion. In de Wit the numerical solutions of these equations for a couple of representative examples are given, as well as the corresponding analytical solutions to the linearized equations. In this communication it is shown how two of the four equations can be solved analytically; these solutions can be used to obtain approximate analytical solutions to the remaining two equations.