A study is made of a floating or submerged body with longitudinal and transverse symmetry, which is moving with constant forward speed and performing small oscillations. The analysis is quite general in the sense that the shape of the body and the nature of the oscillations are unspecified, but it is assumed that the linearized free-surface condition holds. With this assumption the oscillatory velocity potential is found in terms of an unknown Green's function, the existence of which is also assumed. This potential is then used to show the symmetry properties of the cross-coupling damping coefficients.

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