The external forces and stiffnesses acting on each body are specified with respect to the local structure axes (LSA) for that body, whose origin is located at, and moves with, the center of gravity of the body, while the axes remain parallel to the fixed reference axes (see Axes Conventions). Aqwa employs an iterative approach for determining the equilibrium position of the floating system.

Gravitational forces acting on structures are included in the equilibrium position estimation.

At each iterative step, Aqwa calculates hydrostatic forces and moments directly from the integral of hydrostatic pressure over all the elements comprising the submerged part of the body (in the same manner as used in the radiation/diffraction analysis, see Hydrostatic Forces and Moments). You may also directly input a buoyancy force, which is assumed to be constant throughout the analysis.

In multi-directional waves, the mean drift forces are determined from Equation 5–22 by the superposition of wave component series with the same frequency increment.

Aqwa assigns a unique set of pseudo-random numbers to describe the wave component phases within each sub-directional spectrum. However, as Aqwa can only allow a finite number of wave components for each spectrum, the numerical results may be sensitive to the selected wave component number. Statistically, given that the wave component phases follow a uniform random distribution in the range [0, 360] degrees, the mean drift force could be written as:

(11–1)

where is the sample sequence number. For a pair of sub-directions (where m ≠ n), in the limit:

(11–2)

This means that as the number of samples tends to infinity, the mean drift force is independent of any directional coupling effect. Taking this observation into account, for any specified sea state, we introduce

(11–3)

where is the number of random phase settings.

With this form, the numerical results for mean drift forces due to directional coupling are less sensitive to the selected wave component number. Equation 11–3 could alternatively be considered as the summation of the sub-components within a normal wave component frequency range.

In order to estimate the multi-directional coupling mean drift force, the same starting and finishing wave frequencies, and frequency increment are required for all wave directions. Denoting the starting and finishing frequencies of each sub-directional wave spectrum as and respectively, and the number of wave components as , the corresponding values for the whole wave spectral group are determined as

(11–4)

where is the constant frequency increment within the wave spectral group, and is the maximum number of wave components allowed in Aqwa.

A number of thruster forces (, , ) may be included in the equilibrium calculation and can be specified at the positions (, , ) on each structure in the local structure axes (LSA). The magnitudes of the thruster forces are assumed to be constant throughout the analysis. The three components (, , ) define the thruster direction relative to the structure, which is also assumed to be constant. This means that the thruster direction relative to the fixed reference axis system (FRA) will change with the structure position.

As discussed in Axis Transformation and Euler Rotations, the Euler rotation matrix at an intermediate position in the iterative process may be defined from Equation 1–7. Further introducing a 3×3 matrix based on the thruster position in the local structure axes (LSA), i.e.

(11–5)

the thruster force and corresponding moments about the structure center of gravity in the fixed reference axes (FRA) can be given by

(11–6)

where is a 6×1 matrix consisting of three thruster force components and three thruster moment components about the structure center of gravity in the FRA.

Drag effects on mooring lines are ignored if cable dynamics are not used for composite catenary lines.

Steady wind and current drag forces and moments are included, as discussed in Current and Wind Hull Drag, as well as drag forces and moments on Morison elements (see Effects of Morison Elements in Equilibrium and Static Stability Analysis).

Mooring forces and articulation reaction forces are also included.