**1. The problem statement, all variables and given/known data**
This is a basic question to a kind of complex problem, any help will be deeply appreciatted. I have all the motion equations for the system described below, but i have a problem with the reference frames...

So the problem is as follows:

A small wind generator is protected against high speed winds by autofurling mechanism that depends on the equilibrium of torques between the tail and the moment of inertia generated by wind when it hits the rotor:

the diagrams

THE COORDINATE FRAMES

1. inertial frame F_A=a_1, a_2, a_3 point in the average direction of the wind.

2 F_bframe of reference attached to nacelle before tilting

b_1 = a_1 cos (theta) + a_2 sin (theta)

b_2 = - a_1 sin (theta) + a_2 cos(theta)

b_3 = a_3 vertical upward

3 F_C=c_1, c_2, c_3 after tilting

4 F_D = d_1, d_2 ,d_3 aligned with the tail hinge

**2. Relevant equations**
What are the equations for the different the different coordinate systems?? i have the equations for the coordinate system Fb, but when i derived them following the diagrams i got different relations, are the equations given to me wrong or what i'm doing is wrong?

**3. The attempt at a solution**
So for the coordinate system F_B, according to the diagrams i get that:

b_1 =a_1 sin (theta) - a_2 cos(theta)

b_2 =a_1 cos(theta) + a_2 sin(theta)

b_3 = a_3

since i don't get the same result for reference frame b, i'm prety doubtful of what i get in c and d.

Thanks in advance...