LARGE-AMPLITUDE MOTION OF AN ELONGATED BODY IN SHALLOW WATER

A large-amplitude motion of a body of revolution in shallow water is analyzed by assuming the bottom to be even and the Froude number to be large enough for the velocity potential to vanish on the undisturbed free surface. First, the classical Kirchoff-Lagrange equations of motion are extended to the case of time-dependent added-mass and inertia coefficients. The hydrodynamical force and moment acting on the body are expressed in terms of these coefficients together with their partial derivatives with respect to the generalized coordinates of the body. It is demonstrated how these expressions can be applied for the case of a prolate spheroid maneuvering in shallow water, where useful analytical expressions for the hydrodynamical coefficients are also obtained. By employing the concept of "equivalent spheroid" it is also shown that these results are universal in the sense that they may serve as useful approximations for arbitrary smooth bodies with axial symmetry. The hydrodynamical coefficients are given as a product of two terms, one which depends on the geometry of the body and the second on the relative position of the body with respect to the free surface. Both analytical and graphical solutions for these two functions are presented herein and it is also suggested how these can be used for a large-amplitude motion of nonspheroidal bodies of revolution.