Corotational derivative of a polar vector ($D_t\mathbf{p}+\Omega \mathbf{p}$)

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.