Generalizations
It is also possible to use these equations if the axes in which
is described are not connected to the body. Then ω should be replaced with the rotation of the axes instead of the rotation of the body. It is, however, still required that the chosen axes are still principal axes of inertia. This form of the Euler equations is useful for rotation-symmetric objects that allow some of the principal axes of rotation to be chosen freely.
Read more about this topic: Euler's Equations (rigid Body Dynamics)