Using Earth$-$fixed co$-$ordinates defined in class $(e_z$ down, $e_x$ and $e_y)$ perform NASA$-$

standard Euler rotations: yaw $()$ first, pitch $()$ second and roll $()$ last.

Define the angular velocities about the resulting body fixed axes:

${?}^E{}^B=P{b}_x+Q{b}_y+R{b}_z$

a$)$ Solve for the relationships between ${}^{},{}^{},{}^{},$ and $P,Q,R,$ which are called the

'Kinematic Equations'.