= Bottom-heavy spherical-cell orientation dynamics
{title2=$\dot{\mathbf p}=B^{-1}(\mathbf k-p_3\mathbf p)+\boldsymbol\omega\times\mathbf p/2$}
For a spherical cell with its <centre of mass> displaced by $-\ell_g\mathbf p$ from its geometric centre, gravity produces <torque> $mg\ell_g\mathbf p\times\mathbf k$. Rotational resistance $\zeta_r$ gives angular <velocity> $\boldsymbol\omega/2+(mg\ell_g/\zeta_r)\mathbf p\times\mathbf k$. Taking its cross product with $\mathbf p$ gives the displayed orientation equation with $B=\zeta_r/(mg\ell_g)$. Steady orientation therefore requires the two terms on the right to sum to zero; placing the <vorticity> term alone on the other side changes its sign.
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