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Primed stability derivatives
The rolling and yawing motions are coupled through the cross inertia IXZ due to rotation not being about the principal axes. Since in general aircraft are symmetrical about the XZ plane and so IXY = IY 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:
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