Corotational derivative of a polar vector
= Corotational derivative of a polar vector
{title2=$D_t\mathbf p+\Omega\mathbf p$}
With <velocity gradient> $A_{ij}=\partial_i v_j$, set $\Omega=(A-A^T)/2$. A vector rigidly rotating with the material has <material derivative> $D_t\mathbf p=-\Omega\mathbf p$, so its corotational derivative vanishes. Its unit rotational coefficient is fixed by an <objective time derivative>; adding $-\xi D\mathbf p$ describes the material's <flow alignment of a polar order parameter>.