This paper considers the damping and wave resistance of a thin ship which is moving in calm water with constant velocity and oscillating in pitch and heave. The velocity potential is obtained from Green's theorem after a process of systematic linearization in terms of perturbation parameters representing the beam-length ratio and the oscillation amplitude. An asymptotic expansion of the Green's function is derived from which the energy radiation is obtained. The coefficients of damping and increased wave resistance are then found by separation of the energy components. No separation of the two cross-coupling damping coefficients is obtained, however. Calculations are presented for a polynomial hull and compared with experimental data.

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