= Solution
At $\xi=0$, the <polar order parameter> obeys
$$
\dot\theta=-\frac g2,\qquad \dot p=-\Gamma(a+bp^2)p.
$$
For $a<0$, $b>0$, the magnitude relaxes to $\sqrt{-a/b}$ while the direction rotates continuously. Thus the likely ordered behaviour is \b[tumbling rather than a fixed alignment].
More generally, for $|\xi|<1$ and $g\ne0$, $\xi\cos2\theta-1$ never vanishes, so the <tumbling of a polar order parameter> persists. The <polar order parameter> completes a full $2\pi$ rotation in
$$
\boxed{T_{\rm polar}=\frac{4\pi}{|g|\sqrt{1-\xi^2}}},
$$
obtained by integrating $dt=2\,|d\theta|/(|g|(1-\xi\cos2\theta))$ over a full rotation. An unoriented <nematic director> repeats after half this period, whereas a <polar order parameter> distinguishes opposite directions. For $\xi\ne0$ its magnitude can also oscillate. If the <polar order parameter> decays to zero, its orientation is no longer a physical observable; the tumbling conclusion concerns a persistent ordered state.
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