The relative motion of two adjacent bodies, one significantly larger than the other, floating in waves, with a nonlinear connection

New equations of motion are introduced for two adjacent bodies, floating in waves, subject to hydrodynamic interaction. These equations are based on the impulse response function technique discussed by W. E. Cummins (1962) for single-body motion and extends his work to the two-body problem. It is shown how this impulse response function solution and the linear diffraction theory solution proposed by G. Van Oortmerssen (1979) are related. The new equations of motion are then solved numerically for the special application of lifting a deep submergence research submarine aboard a mother vessel equipped with a stern mounted A-frame, and the dynamic loading on the lift system is determined. A byproduct of this solution is the determination of limiting sea conditions for conducting a safe recovery and an evaluation of various lift system equipment options. Finally, the numerical solution is compared with an at-sea instrumented test and found to be in close agreement for similar sea conditions.