GENERALIZED KIRCHHOFF EQUATIONS FOR A DEFORMABLE BODY MOVING IN A WEAKLY NONUNIFORM FLOW-FIELD

The classical Kirchhoff's method provides an efficient way of calculat ing the hydrodynamical loads (forces and moments) acting on a rigid bo dy moving with six-degrees of freedom in an otherwise quiescent ideal fluid in terms of the body's added-mass tensor. In this paper we provi de a versatile extension of such a formulation to account for both the presence of an imposed ambient non-uniform flow field and the effect of surface deformation of a non-rigid body. The flow inhomogeneity is assumed to be weak when compared against the size of the body. The cor responding expressions for the force and moment are given in a moving body-fixed coordinate system and are obtained using the Lagally theore m. The newly derived system of nonlinear differential equations of mot ion is shown to possess a first integral. This can be interpreted as a n energy-type conservation law and is a consequence of an anti-symmetr y property of the coefficient matrix reported here for the first time. A few applications of the proposed formulation are presented includin g comparison with some existing limiting cases.