Is calculating the Euler angles analitically possible?(adsbygoogle = window.adsbygoogle || []).push({});

I am trying to obtain the angles to transform the body-fixed reference frame to the inertial reference frame. I can get them without problems with numerical methods. But I would to validate them analitically, if possible.

I followed the steps by Landau & Lifshitz (https://archive.org/stream/Mechanics_541/LandauLifshitz-Mechanics#page/n123/mode/2up) and found the angular velocity in the body frame. Which is also here.

Now, I understand that when the angular momentum vector is aligned with the inertial Z axis, then the angle rates are:

$$ \dot{\theta} = 0 $$ $$ \dot{\phi} = M/I_1 $$ $$ \dot{\psi} = M\cos \theta (1/I_3 - 1/I_1) $$

But what if the angular momentum and the Z axes are not aligned? When this happens, ##\theta## stops being constant, doesn't it?

Thank you in advance!

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# I Euler angles in torque free precession of a symmetric top

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