Solution
= Solution
For the <symmetric top>, set $I_1=I_2=J$. The third of <Euler's equations (rigid body dynamics)> reduces to $I_3\dot\omega_3=\tau_3=0$. Thus the axial <angular velocity> component is a <conserved quantity>:
$$
\boxed{\omega_3(t)=\omega_3(0).}
$$
The transverse <angular velocity> components are generally variable. A <torque> constant in the <principal body frame> generally rotates in the <inertial frame>; constancy in the two frames is different.