- #1
omer21
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Homework Statement
[itex]B(u,u)=\int_{0}^{L}a\frac{du}{dx}\frac{du}{dx}dx[/itex]
B(.,.) is bilinear and symmetric, δ is variational operator.
In the following expression, where does [itex]\frac{1}{2}[/itex] come from? As i know variational operator is commutative why do not we just pull δ to the left?
[itex]B(\delta u,u)=\int_{0}^{L}a\frac{d\delta u}{dx}\frac{du}{dx}dx=\delta\int_{0}^{L}\frac{a}{2}\left(\frac{du}{dx}\right)^{2}dx=\frac{1}{2}δ\int_{0}^{L}a\frac{du}{dx}\frac{du}{dx}dx=\frac{1}{2}δ\left[B(u,u)\right]
[/itex]