Recall, the Eulerian angles that we defined in class as shown below. The axes (i, j, k) are fixed in body frame B and the axes (Î, Ĵ, K)of B

with respect to mathF is represented through the angles (ø, 0, v) using a sequence about intermediate z, intermediate y and intermediate z-axis again to obtain body-fixed frame B in the final configuration, from the inertial reference frame F. This is often referred to as 3-2-3 sequence are fixed in the inertial reference frame F. The orientation or z-y-z sequence. You are hired as an control and navigation engineer at a satellite manufacturing firm. The satellite is equipped with thrusters which can rotate it about all the possible axes in the intermediate body-fixed frame at any given instant instead of just the y and z-axes. Now, there is a requirement to use a 2-1-3 sequence or the y-x-z sequence of successive rotations about the intermediate axes, \boldsymbol{F} \stackrel{\hat{J} \text { or } \hat{n}_{12}, \phi}{\longrightarrow} \mathbf{F}_{1} \stackrel{\hat{n}_{11} \text { or } \hat{n}_{21}, \theta}{\longrightarrow} \mathbf{F}_{2} \stackrel{\hat{n}_{23} \text { or } \hat{j}, \psi}{\longrightarrow} \mathbf{B} 1. Write down the individual rotation matrices for each of the Eulerian angles, i.e. Tó, Tạ, Ty. 2. Write the simplest angular velocity vector wB/F in terms of Euler angles according to the2-1-3 rotation sequence. Remember, the simplest expression is always written using basis vectors of intermediate reference frames. 3. Express the angular velocity vector wB/F in the second intermediate reference frame, F2, i.e.in terms of (în21, Ñ22, îÑ23)