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Math Help - Dynamics of a beam

  1. #1
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    Post Dynamics of a beam

    Relevant to the dynamics of a beam, consider the fourth order linear differential operator.
    L=\frac{d^4}{dx^4}
    a. Show that uLv - vLu is an exact differential. It is a differential of an expression with four terms, each term a product of u and v or their derivatives.
    b. Evaluate \int \begin{array}{cc}1\\0\end{array} (uLv - vLu) dx in terms of boundary data for any functions u and v.
    Please help
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  2. #2
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    This should get you started

    u \frac{d^4v}{dx^4} - v \frac{d^4u}{dx^4} = \dfrac{d}{dx} \left(u \frac{d^3v}{dx^3} - v \frac{d^3u}{dx^3} -  \frac{du}{dx} \frac{d^2v}{dx^2}+   \frac{dv}{dx} \frac{d^2u}{dx^2}\right)
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  3. #3
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    thank you
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