= Hydrodynamic centre of a two-sphere dumbbell
{title2=$\mathbf r_c=(a_1\mathbf r_1+a_2\mathbf r_2)/(a_1+a_2)$}
Two widely separated spheres rigidly joined by a hydrodynamically negligible connector obey the <free-draining approximation>. Their translational <hydrodynamic resistance matrix> is $6\pi\mu(a_1+a_2)I$. The displayed point is the centre about which every pure translation has zero <hydrodynamic torque>: $\sum_i\zeta_i(\mathbf r_i-\mathbf r_c)=0$. A pure rotation about that point gives no resultant <force> at this order. This is an exact cancellation within the approximation, rather than an exact formula at arbitrary finite separation. It does not assert that every chiral rigid body has an origin eliminating its translation-rotation coupling.
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