The reciprocal forms of steady wave drift force and moment for a freely floating body in regular waves are derived from the momentum theory. The forms for surge, sway and yaw are similar. The expressions in the near field and in the far field are similar too except for sign. The forms consist of the first order solutions, that is, the quadratic terms of linear solutions. The expression in the near field contains the gradient of velocity potential and its normal derivative on the body surface. The scheme to calculate the gradient of velocity potential and its normal derivative based on the constant panel method is shown. Numerical examples and comparison of wave drift forces calculated by Maruo's and Newman's far field method, Pinkster's near field method and present reciprocal form are shown. From these results the new calculation method seems to be valid.
Some relations between radiation waves and hydrodynamic forces acting on a floating body in waves are known (Mei, 1989). For example, Haskind relation, the symmetry of radiation forces, the relation between damping coefficient and Kochin function, etc.. They are derived by applying Green's theorem to appropriate pairs of wave potentials in fluid volume systematically. Table 1 shows the reciprocity relations and pairs of functions to be applied Green's theorem to in control fluid volume, where ϕ D = ϕ0 + ϕ7 is the diffraction wave, ϕ j the radiation wave, f ij the coefficient of radiation forces and ϕ(χ A) the total wave including the incident wave with angle χ A. It should be noted that the order of the amplitude square can be considered in applying the Green's theorem to a pair of functions. Kashiwagi (2006) derived two relations between Kochin functions of a freely floating body in regular waves by applying Green's theorem to a pair of ϕ(χ A) and ϕ(χ B), and another pair of ϕ(χ A) and ϕ(χ B).