1. A pilot is flying an aircraft with an XZ plane of symmetry. Let $I_{xx} = I_{yy} = I_{zz} = 1/3$ and $I_{xz} = 1/6$. The aircraft begins at the equilibrium point of steady rectilinear flight (See Schmidt page 484). Note that you should use the body frame. Not the stability frame like is done on Schmidt page 484. The pilot wants to rotate the aircraft in the positive direction around one of the body frame axis. To accomplish this goal the pilot applies a positive torque around the axis which they want to rotate around. All other torques are zero. For each of the following cases give the sign (positive, negative, or zero) of $P$, $Q$, and $R$ immediately after the torque is applied. In each of these cases, does the pilot accomplish their goal? Note: The pilot only wants to rotate around one of the axis not multiple. The pilot does not accomplish their goal if there is rotation around any axis other then the one desired. Explain fully your reasoning and assumptions.
i. Desired rotation around the body frame $X_A$ axis.
ii. Desired rotation around the body frame $Y_A$ axis.
iii. Desired rotation around the body frame $Z_A$ axis.
