1.
a) Using the Z - Y - X (a - -y) Euler angle convention, write a MATLAB program to calculate the rotation matrix AR when the user enters the Euler angles a - -- y. Test for two examples:
(i) a = 10, = 20, y = 30 (ii) a = 30, = 90, y = -55
For case (i), demonstrate the six constraints for unitary orthonormal rotation matrices (i.e., there are nine numbers in a 3 x 3 matrix, but only three are independent). Also, demonstrate the beautiful property, AR = R-1 = ART, for case (i).
b) Write a MATLAB program to calculate the Euler angles a -- -- y when the user enters the rotation matrix AR (the inverse problem). Calculate both possible solutions. Demonstrate this inverse solution for the two cases from part (a). Use a circular check to verify your results (i.e., enter Euler angles in code a from part (a); take the resulting rotation matrix gR, and use this as the input to code b; you get two sets of answers -- one should be the original user input, and the second can be verified once again using the code in part (a). c) For simple rotation of about the Y axis only, for = 20' and P = [1 01]T calculate Ap.