= Initial curvature incompatibility at a moment-free beam end
A prescribed initial beam profile may vanish at a pivot while having nonzero endpoint <curvature>. If the post-release pivot is moment-free, its <bending moment> condition is $EIy_{xx}=0$. The data then cannot have a classical solution with continuous <curvature> at the initial boundary corners. A finite-energy <weak solution> can still represent release from preparing end moments. For example $y_0=ax(x-L)$ has odd <sine> coefficients proportional to $n^{-3}$; $\sum n^4|A_n|^2$ converges, giving finite bending <energy>. The <displacement> series takes the prescribed initial shape, but termwise endpoint second <derivatives> cannot be identified with its interior <curvature> limit. This conservative beam evolution does not have the immediate smoothing of a <heat equation>.
Back to article page
