HW I $($conti$.)$

Consider the Euler angles involved in a $321$ rotation from $F_W$ to $F_B.$

For the initial $(F_w)$ and each intermediate coordinate system involved in this ansformation, determine which, if any, of the axes lie in one of the three planes rmed by pairs of axes of $F_B.$ Describe and sketch each case identified and xplain why it is so$.$

J$)$ What is the value of ${}_x$ in the transformation? Explain.

Compare these rotations with the definitions of the aerodynamic angles $$ and $3,$ and verify that the names of the Euler angles given for $T_{B,w}$ are correct.

d$)$ Verify that the transformation matrix from wind to body axes is

$5-$ Consider the square metal sheet and the Cartesian coordinate system shown ingthe figure below. The proposed plane stress solution is

$($a$)$ Determine whether or not the proposed plane stress solution is actually a solution within the interior of any homogeneous, isotropic, linearly elastic body

$($b$)$ Determine the tractions $T_x$ and $T_y$ on the upper right hand edge surface where

$T_n-{}_{x}cos(n,x)+{}_{xy}cos(n,y)$

$T_y={}_{xy}cos(n,x)+{}_{y}ycos(n,y)$

$\frac{\frac{\text{d}\text{e}\text{l}{}_0}{a}(y-x)}{\text{d}\text{e}\text{l}}+\frac{\frac{\text{d}\text{e}\text{l}{}_0}{a}(1-x)}{\text{d}\text{e}\text{l}}+\frac{a}{?}$