= Rotational constraint correction to sphere mobility
In the preceding two-sphere geometry, holding the second sphere's angular velocity at zero needs a torque $\mathbf G=-4\pi\mu a^3\boldsymbol\omega_\infty$. Its <rotlet> adds
$$
\delta\mathbf U_{\rm rot}=-\frac{3a^4}{4R^4}
\left[\mathbf U_0-(\mathbf U_0\cdot\widehat{\mathbf R})\widehat{\mathbf R}\right]
$$
to the first sphere's velocity, in addition to the <self-mobility correction from a distant force-free sphere>. This leading constraint correction is transverse to the line of centres.
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