Figure $\mathrm{.}1.$ Coordinate systems and forces$/$moments acting on a quadrotor.

a$)$ Draw the inertial frame $\backslash (\backslash$mathbb$\{$I$\}\backslash )$ and a quadcopter fixed frame $\backslash (\backslash$mathbb$\{$J$\}\backslash )$;

b$)$ Identify the state vector and the control input;

c$)$ Write the equations of motion of the quadcopter;

d$)$ Find an equilibrium point for the quadcopter $($hint: when quadcopter is in hovering

e$)$ Linearize the equations of motion about this equilibrium point.