February 2, 2017
Agreed, the three components of any lab frame torque must be transformed to the moving frame torque used in the Euler equations, using Eq. (11), and the three equations solved simultaneously for the trajectories of the Euler angles, theta(t), ph(t) and chi(t). The problem is written out in full in Note 368(8). In my computer simulation work, the frame transformation for each molecule is carried out with a transformation matrix based on unit vectors in the princiapl moments of inertia, instead of using the Euler angles.”
You do realize, we hope, that the angular momentum vector of a precessing spinning-top rarely coincides with the physical axis of the top. To assume so would be a really embarrassing tyro error to make.