DynCont#5 Fixed and relative frames of reference in high speed shafts

1.  We always measure the speed only in the fixed frame of reference, inertial, non accelerating, constant velocity.
2. It is easier to do integration in ground fixed, inertial frame of reference.
3. But for a whirling shaft / tumbling body, the mass moment of inertia along the x axis of fixed frame of reference keeps changing due to the tumbling of the disk,even though the disk is rigid.
4. For an axis system that is aligned to the disk at a particular instant in time, not fixed to the disk, the mass moment of inertia along the x axis of the aligned system is constant.
5. But it is difficult to do time integrations along this axis system that is aligned to the disk 
6. Again, we are only measuring with respect to ground fixed reference system. That value, we are expressing in terms of an axis system that is aligned to the disk at that particular instant of time. This is only to use the inertia defined in the disk aligned axis system. With this kinetic energy, we can write the Lagrange governing equation and then derive the fundamental equation of motion.