Corotating-frame representation of a Jaumann derivative ($\frac{d}{dt}(Q^{T}TQ)=Q^T\stackrel{\circ }{T}Q$)

If an orthogonal matrix $Q$ satisfies $\dot{Q}=WQ$ for the spin tensor $W^T=-W$, the Jaumann derivative becomes an ordinary derivative in that frame:This follows by differentiating all three factors and using ${\dot{Q}}^T=-Q^{T}W$. It converts a tensor relaxation law using the Jaumann derivative into a componentwise ordinary differential equation.