Flow-alignment angle in planar shear ($\cos 2\theta =1/\xi$)

For a uniform polar order parameter in simple shear flow $\mathbf{v}=(gy,0)$, the angular equation is $\dot{\theta }=g(\xi \cos 2\theta -1)/2$. A fixed orientation for nonzero shear therefore requires $|\xi |\ge 1$. For $|\xi |>1$, its angular stability condition is $g\xi \sin 2\theta >0$; equality at $|\xi |=1$ requires nonlinear analysis. The ordered magnitude must separately satisfy the radial stationarity equation and be nonzero.