For free symmetric top $I_1=I_2\neq I_3$, the solution was $\vec\omega(t)= A\sin(\Omega t) \vec e_1 +A\cos(\Omega t)\vec e_2 +\omega^3_0 \vec e_3$ where $\vec \omega(0)=(0,0,\omega_0^3)$ was the initial angular vlelocity, $\vec e$ were body frame, and $\tilde e_3$ were lab frame. as in the usual solution.

Prove that, if $A\neq 0$, then $\vec e_3$ rotates around $\tilde e_3$ with angular velocity $\Omega$.

  • $\begingroup$ Calculate the angle between $\vec e_{3}$ and $\vec \omega$. $\endgroup$ – Cinaed Simson Nov 21 '19 at 21:47

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