(Solved): a. (1.5 points) Using the ZYX() Euler angle convention, write a MATLAB program to ...

a. (1.5 points) Using the $Z-Y-X(\alpha -\beta -\gamma )$ Euler angle convention, write a MATLAB program to calculate the rotation matrix $R$ when the user enters the Euler angles $\alpha -\beta -\gamma$. Test for two examples i) $\begin{array}{lll}\alpha =10^{\circ },& \beta =20^{\circ },& \gamma =30^{\circ }.\\ \alpha =30^{\circ },& \beta =90^{\circ },& \gamma =-55^{\circ }.\end{array}$ b. (1.5 points) Write a MATLAB program to calculate the Euler angles $\alpha -\beta -\gamma$ when the user inputs the rotation matrix $R$ (the inverse problem). Demonstrate this inverse solution for the two cases from part 2.2.a.