= Orientation averaging of an axisymmetric stresslet
{title2=$\langle S(\mathbf e\mathbf e-I/3)\rangle=-\tfrac S2(\mathbf n\mathbf n-I/3)$}
The angular factor of an axial <stresslet> is linear in the <symmetric traceless rank-two tensor> $\mathbf e\mathbf e-I/3$. Hence averaging a collection of directors amounts to averaging this tensor. For uniformly distributed in-plane directions, $\langle\mathbf e\mathbf e\rangle=(I-\mathbf n\mathbf n)/2$, so $\langle S(\mathbf e\mathbf e-I/3)\rangle=-(S/2)(\mathbf n\mathbf n-I/3)$. The averaged director is normal to the plane and its signed strength is reversed and halved.
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