7. Assume a rigid aircraft with plane of symmetry $x_B - z_B$. The sideslip and angle-of- attack with respect to a given body-axis system are free to vary. Consider the wind-axis moment equation,
$\{M\}_w = \mathbf{h}^* + I_w \{\omega\}_w + I_w \{\dot{\omega}\}_w + \{\Omega\}_w \mathbf{h}^* + \{\Omega\}_w I_w \{\omega\}_w$
Identify each term that vanishes in body axes but not in wind axes, and briefly explain why they do not vanish.
8. Assume a rigid aircraft with plane of symmetry $x_B - z_B$. Consider two body-fixed coordinate systems, $F_{B_1}$ and $F_{B_2}$, related by a positive rotation about $y_B$ through angle $\epsilon$, positive from $F_{B_1}$ to $F_{B_2}$. Further assume the axes of $F_{B_1}$ are $F_P$, the principal axes of the aircraft, and that the values of the principal moments of inertia $I_{xp}$, $I_{yp}$, and $I_{zp}$ of the inertia matrix $I_P (= I_{B_1})$ are known. Transform the inertia matrix $I_P$ into $F_{B_2}$, and determine expressions for each of the moments of inertia of the aircraft in $F_{B_2}$ in terms of the principal moments of inertia.
9. Assume $F_B = F_P$. Find an expression for $I_{xy}$ in $F_w$, in terms of $\alpha$, $\beta$, $\dot{\alpha}$, $\dot{\beta}$, and the principal moments of inertia.
