When dealing with problems in the frequency domain, we are concerned with small-amplitude motions about an equilibrium floating position. Thus, the wetted surface of the body becomes time-independent and the hydrostatic forces and moments about the mean position of the body must be computed. This is done using the above equations. Obviously, the prescribed position must be one which allows the body to take up an equilibrium position in the still fluid. The equilibrium position will be dependent on the mass and mass distribution of the body combined with the distribution of hydrostatic pressure. The distribution of hydrostatic pressure may be described in terms of the total upward buoyant force and the position of the center of buoyancy. For an equilibrium state to exist, the following static conditions must be true:
The weight of the body must be equal to the total upward force produced by buoyancy. Lateral force components must also sum to zero. If the only forces acting on the body are gravity and hydrostatic pressure (as the free-floating body is here), then the weight of the body must equal the upward buoyant force:
(3–5)
where
is the total structural mass of the floating body
and 
is the structural mass distributed at the location
of 
.The moments acting on the body must sum to zero. If the moments are taken about the center of gravity, then the buoyancy moment and the moment of all external static forces must be zero:
(3–6)
where the center of gravity
is estimated with the
mass distribution 
(3–7)
Again, if the only forces acting on the body are gravity and hydrostatic pressure, then the center of gravity and the center of buoyancy must be in the same vertical line when the free-floating body is at equilibrium position in still water; in other words,
 | (3–8) |
Otherwise, if the prescribed body position is not at the equilibrium location, the out-of-balance force and moment are output in the forms of
 | (3–9) |
in which the out-of-balance force and moment are divided by the weight of the body and are with respect to the intermediate coordinate frame GXYZ introduced in Axis Transformation and Euler Rotations for Euler rotations.