From the physical standpoint the added-mass coefficients represents the amount of fluid accelerated with the body. However, the added-mass coefficients for translation generally differ depending on the direction of the body motion, as opposed to Newton's equation
where the body mass
is independent of the direction of the acceleration
.
Also, in the absense of body symmetry, the cross-coupling coefficients such as
and
are non-zero, implying that the hydrodynamic force differs in direction from the acceleration.