Dynamic equations of motion for a rigid or deformable body in an arbitrary non-uniform potential flow field

In this paper we present a general method for calculating the hydrodynamic loads (forces and moments) acting on a deformable body moving with six degrees of freedom in a non-uniform ambient potential flow field. The corresponding expressions for the force and moment are given in a moving (body-fixed) coordinate system. The newly derived system of nonlinear differential equations of motion is shown to possess an important antisymmetry property. As a consequence of this special property, it is demonstrated that the motion of a rigid body embedded into a stationary flow field always renders a first integral. In a similar manner, we show that the motion of a deformable body in the presence of an arbitrary ambient flow field is Hamiltonian. A few practical applications of the proposed formulation for quadratic shapes and for weakly non-uniform external fields are presented. Also discussed is the self-propulsion mechanism of a deformable body moving in a non-uniform stationary flow field. It leads to a new parametric resonance phenomenon.