= Straight-rod resistance in a linear flow
{title2=$C=4\pi\mu/|\log\epsilon|$}
For a straight rod $\mathbf X=s\mathbf p$, $-L<s<L$, leading <slender-body theory> uses $\mathbf f=C(I-\mathbf p\mathbf p/2)[\Delta\mathbf U+s(\Delta\boldsymbol\Omega\times\mathbf p-E\mathbf p)]$. Integration gives $\mathbf F=2CL(I-\mathbf p\mathbf p/2)\Delta\mathbf U$ and $\mathbf G=(2CL^3/3)[(I-\mathbf p\mathbf p)\Delta\boldsymbol\Omega-\mathbf p\times E\mathbf p]$. Axial spin is outside this centreline approximation.
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