Symmetry-axis equation of a heavy symmetric top
= Symmetry-axis equation of a heavy symmetric top
Writing the unit symmetry axis as $n$ and axial spin momentum as $s=I_3\omega_3$, <angular momentum> is $L=I_1n\times\dot n+sn$. Taking its derivative and applying gravitational <torque> gives $I_1n\times\ddot n+s\dot n=-mg\ell n\times\widehat z$.