MdATLAB EXERCISE $2$A

a$)$ Using the $Z-Y-x(--)$ Euler angle convention, write a MATLAB program

to calculate the rotation matrix ${?}_B^{A}R$ when the user enters the Euler angles $--.$

Test for two examples:

i$)=10,=20,=30.$

ii$)=30,=90,=-55.$

For case $($i$),$ demonstrate the six constraints for unitary orthonormal rotation

matrices $($i$.$e$.,$ there are nine numbers in a $33$ matrix, but only three are

independent$).$ Also, demonstrate the beautiful property, ${?}_A^{B}R={?}_B^A{R}^{-1}={?}_B^A{R}^T,$

for case i$.$

MATLAB Exercise $2$B

b$)$ Write a MATLAB program to calculate the Euler angles $--$ when the user

enters the rotation matrix ${?}_{}^{A}R($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 ${?}_B^{A}R,$ 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 by once again using the code in part $($a$).$Sdd