- #1

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Here's my problem:

Let's suppose that we have a functional [itex]I[f,g]=\int{L(f,\dot{f},g,\dot{g},x)\,dx}[/itex].

Is it right to say that the variation of [itex]I[/itex] whit respect to [itex]g[/itex] (thus taking [itex]g\;\rightarrow\;g+\delta g[/itex]) is [tex]\delta I=\int{[L(f,\dot{f},g+\delta g,\dot{g}+\delta \dot g,x)-L(f,\dot{f},g,\dot{g},x)]\,dx}=\int{(\frac{\partial L}{\partial g}\delta g+\frac{\partial L}{\partial \dot{g}}\delta \dot{g})\,dx}[/tex]??

Thanks for your disponibility!