Primed stability derivatives
The rolling and yawing motions are coupled through the cross inertia I_{XZ} due to rotation not being about the principal axes. Since in general aircraft are symmetrical about the XZ plane and so I_{XY} = I_{Y }Z = 0 coupling of this sort usually only exists between the roll X and yaw Z axes.
The equations of motion may be simplified by expressing them in terms of primed stability derivatives which are modified L and N derivatives obtained using the cross inertias and the corresponding derivative of the other axis. Thus the primed roll derivatives are: