Consider a rigid $SC$ with the given inertia tensor and other information given in the body

coordinate system.

$1-1$ Determine the SC rotational kinetic energy $($RKE$)$ and its moment of inertia about the given vec$(),$

vector.

$1-2$ Determine the SC Principal MOIs, the associated rotation matrix $($between the body and the principle

axes$),$ as well as the corresponding Euler angles between the two BCSs$.$

$1-3$ Determining and draw the SC ellipsoid of inertia.

$1-4$ Determine and draw the SC AM and KRE ellipsoids for the given energy.

$1-5$ Plot$/$show the intersection between the AM and KRE ellipsoids $($Polhode curves$).$

$1-6$ Optional Bonus: Present mathematical formulas for the Polhode curves.