Formulation of the problem of the motion of a small body in a perturbed flow

The classical problem of the hydrodynamic reactions on a body of arbitrary shape moving in a fluid at rest was generalized by Sedov to the case of an accelerated translational flow. In the expressions for the hydrodynamic reactions, the shape of the body is represented only by the coefficients lambda sub(ij) of the added masses and the volume Omega of the body. In the general case of motion of a body in a nontranslational flow the shape of the body cannot be represented by a finite set of coefficients in the determination of the hydrodynamic reactions. An important simplification occurs in the small-body formulation, which again leads to expressions for the force and torque similar to the classical expressions. In the present paper it is shown that if it is additionally required that the final expression for the reactions should contain only principal terms containing the components v sub(i) and omega sub(i) of the translational and angular velocities, and also terms describing the flow structure, then the expression found by Grigoryan and Yakimov for the hydrodynamic reactions is valid.