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Higher-order Euler-Lagrange equation

For the functional

L [y] = \int_{a}^{b} F (x, y, y^{'}, \dots, y^{(m)}) d x,

the vanishing of its first variation under fixed endpoint data gives

\sum_{j = 0}^{m} (- 1)^{j} \frac{d ^{j}}{d x ^{j}} F_{y^{(j)}} = 0.

Table of contents 63 2
- Clamped-free beam under uniform load and endpoint force Higher-order Euler-Lagrange equation 49 1
  - Endpoint force derivative of clamped-free beam energy Clamped-free beam under uniform load and endpoint force 22

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