= Solution
Use the paper's <velocity gradient> convention $A_{ij}=\partial_i v_j$, so $\Omega=(A-A^T)/2$ and $D=(A+A^T)/2$. In a <rigid motion> there is rotation but no <rate-of-strain tensor>: $D=0$. A <polar order parameter> attached to the material must rotate exactly with it. In this convention its <material derivative> is $-\Omega\mathbf p$, and its <corotational derivative of a polar vector> must vanish.
Thus the compensating term is $+\Omega\mathbf p$ with \b[coefficient exactly one]. This follows from an <objective time derivative> and is independent of material properties. By contrast, the response to $D\mathbf p$ describes deformation and <flow alignment of a polar order parameter>; its coefficient $\xi$ can depend on the material. The transposed <velocity gradient> convention is essential to the sign of $\Omega$.
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