= Intrinsic curvature of an elastic filament
{title2=$\kappa_0(s)$}
= Intrinsic filament curvature
{synonym}
The intrinsic <signed curvature> is the curvature of a stress-free filament, measured along material <arc length>. An <elastic filament> with actual curvature $\kappa$ stores bending energy $\frac B2\int(\kappa-\kappa_0)^2ds$, with <filament bending modulus> $B$. In a planar small-slope <Monge representation>, $\kappa\simeq\zeta''$ and the leading energy is quadratic in $\zeta''-\kappa_0$.
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