Euler elastica
= Euler elastica
{c}
{title2=$EI\theta''+F\sin\theta=0$}
The planar equilibrium of an inextensible slender beam can have large tangent <angle> while retaining small elastic <strain> across its thickness. For constant horizontal compressive <force> $F$, moment balance and <curvature> $\theta'=d\theta/ds$ give the displayed nonlinear equation. Multiplication by $\theta'$ gives the first integral $EI\theta'^2/2-F\cos\theta=C$. A tensile load has $F<0$ in this convention.