For an analysis of rigid body motion about a mean equilibrium position, Aqwa requires a hydrostatic stiffness matrix for each body. If the stiffness matrix is expressed in terms of motions about the center of gravity, and only the hydrostatic pressure is considered, the matrix will take the form:

(3–19)

where the various terms in the stiffness matrix are:

where is the cut water-plane area from Equation 3–10 and is the displacement calculated from Equation 3–1.

If the body is in a free-floating equilibrium state with no external forces acting on it, from Equation 3–8 the center of buoyancy and the center of gravity will be in the same vertical line, so that the terms and in the equation above will be zero and the stiffness matrix will be symmetric. The metacentric heights in both the longitudinal and transverse directions may be used to generate the X and Y rotational stiffness terms in the overall hydrostatic stiffness matrix, such that

(3–20)