The reference frame transformation from the LVLH frame to the body frame is usually handled through the use of either Euler angles or quaternions. (a) Write a function in MATLAB to convert Euler angles to quaternions. The name of the function must be e2q. It must take a 3x1 vector of Euler angles as input and output a 4x1 vector of quaternions. Use the function to convert the Euler angles in Table 1 to quaternions. Case 1 2 3 4 5 6 7 8 [] [O] 0 0 -90 90 Case 1 2 0 [] [] 0 -90 0 90 90 0 0 0 30 30 35 85 -125 -50 -155 113 -108 24 Table 1: Euler angles to be converted to quaternions. (b) Write a function in MATLAB to convert quaternions to Euler angles. The name of the function must be q2e. It must take a 4x1 vector of quaternions as input and output a 3x1 vector of Euler angles. Use the function to convert the quaternions in Table 2 to Euler angles. 30 -110 (c) Use the e2q function and the data in Table 1 to verify the output of your q2e function. Discuss any differences between the values in Table 1 and the output of your q2e function. 93 90 91 92 0.1976 0.8673 0.2626 0.3738 0.8500 -0.2505 0.4606 0.0521 Table 2: Quaternions to be converted to Euler angles.