- #1
lennyleonard
- 23
- 0
Hi everyone!
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!
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!