For the hoop shown below with mass m and radius r find the i

For the hoop shown below with mass. m. and radius, r. find the inertial matrix for the x, y, and z axis where the plane of the hoop is misaligned with the xy plane by an angle psi.

Solution

write n= icosalpha + jcos beta +k cos gamma, it is seen that only beta is not zero

so n= jcos beta = j cos phi

Let the matrix I be the momen f inertia of the hoop , ie Ixx, Iyy,I zz, I xz, I xy, Ixz

The transformed inertia can be written as [ o cos phi 0]* I * [ 0 cos phi 0] ^T