= Translation-rotation reciprocal coupling
{title2=$\mathbf F=-A\mathbf U-B\boldsymbol\Omega,\quad\mathbf T=-B^T\mathbf U-C\boldsymbol\Omega$}
For a fixed rigid-body shape and origin in an unbounded stationary <Stokes flow>, the <Lorentz reciprocal theorem> makes the off-diagonal blocks of the six-dimensional <hydrodynamic resistance matrix> transposes. Here $\mathbf F,\mathbf T$ are the fluid's force and torque on the body. If every pure translation has zero <torque> about the chosen origin, then $B^T=0$, hence $B=0$: every pure rotation about that origin has zero resultant <force>. This conditional statement does not require such an origin to exist for every body.
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