AN INITIAL-VALUE PROBLEM FOR THE MOTION OF A SHIP MOVING WITH CONSTANT MEAN VELOCITY IN AN ARBITRARY SEAWAY

The motion of a freely floating or submerged body, which is moving with a constant average forward speed and oscillating arbitrarily in any of the six degrees of freedom, is formulated as an initial-value problem. The seaway is assumed to be arbitrary. The body is assumed to be smooth, but no symmetry of the body is required. The fundamental assumption is that both the free-surface disturbance due to forward motion of the body and the oscillations are small enough so that the problem may be linearized. By an approach similar to that of Wehausen 1965, it is shown how the present treatment of the problem leads also to Ogilvies 1965 modified results of Cummins 1962 decomposition of the velocity potential for the case of an oscillating body with a constant average forward speed. The linearized equations of motion of the body are then derived as a set of six integro-differential equations. Existence and uniqueness theorems are not established either for the boundary-value problem or for the integral equation which is constructed.