= Bending strain of a rod
{title2=$u$}
For planar <director kinematics of a rod> measured in reference <arc length> $S$, define the signed bending strain by $d\mathbf d_3/dS=u\mathbf d_1$. If $s$ is current <arc length> and $\alpha=ds/dS>0$ is the <stretch ratio>, the signed spatial <curvature> is $u/\alpha$: the <chain rule> gives $d\mathbf d_3/ds=(u/\alpha)\mathbf d_1$. Thus bending strain and spatial <curvature> coincide for an <inextensible rod>, but differ in general. An intrinsic value $\hat u$ is the preferred reference-length bending strain in an energy density $B(u-\hat u)^2/2$ per unit reference length.
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