THE IMPULSE RESPONSE FUNCTION AND SHIP MOTIONS

After a review of the deficiencies of the usual equations of motion for an oscillating ship, two new representations are given. One makes use of the impulse response function and depends only upon the system being linear. The response is given as a convolution integral over the past history of the exciting force with the impulse response function appearing as the kernel. The second representation is based upon a hydrodynamic study, and new forms for the equations of motion are exhibited. The equations resemble the usual equations, with the addition of con-volution integrals over the past history of the velocity. However, the coefficients in these new equations are independent of frequency, as are the kernel functions in the convolution integrals. Both representations are quite general and apply to transient motions as well as periodic. The relations between the two representa-tions are given. The treatment considers six degrees of freedom, with linear coupling between the various modes.