Under the small amplitude motion assumption, the basic movements of the internal tank at the LTA origin is expressed in the 6x1 matrix form of , and can be determined by

(3–26)

where is a matrix form of the rigid motions with respect to the combined COG at equilibrium, which is illustrated in Figure 1.4: Floating Rigid Motions , and

From Equation 3–26, it is found that:

.

is the position of the combined COG acquired by Equation 3–26 while , which means it is also the position of the LSA origin in the FRA.

The force and the moment with respect to the LTA origin is expressed as a 6x1 matrix in the form of , which can be transferred as the force and moment with respect to the LSA origin in the FRA,

(3–27)

where is the 6x1 matrix form of the force and moment with respect to the LSA origin.