Problem $4.(20$pts$)$ An airplane is in a constant$-$speed, constant$-$altitude $(u_0=$ constant,

$h_0=$ constant, $w_0=v_0={}_0=0)$ steady turn with a constant roll angle and constant turning rate

$.$ The figure below shows the front view of the flight state. Ignore any effects of rotors internal

to the airplane.

$($a$)$ Show that the the angular rates under above conditions are

$q_0=sin{}_0$

$r_0=cos{}_0$

$p_0=0$

Show all of your steps!

$($b$)$ Determine the expressions for the values of $Y_0,L_0,M_0,$ and $N_0$ at this instantce.

it is important to note here that L$\_0$ M$\_0$ N$\_0$ are the scalar values of the euler moment equations for the moving $($i$.$e$.$ body frame$)$ of the aircraft