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Replacing Lagrangian L with function f(L) for free particle
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[QUOTE="nikolafmf, post: 4958039, member: 284130"] [h2]Homework Statement[/h2] [/B] If L is Lagrangian for a (system of) free particle(s) and dL/dt=0, show that any twice differentiable function f(L) gives the same equations of motions. [h2]Homework Equations[/h2] [/B] Euler-Lagrange equations.[h2]The Attempt at a Solution[/h2] Well, after some calculation, I get [itеx] $\frac{d}{dt}\frac{\partial f}{\partial \dot{r}}-\frac{\partial f}{\partial r}=0$ [/itеx]. Can I conclude from this that f(L) gives the same equations of motion? If not, what should I do? [/QUOTE]
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Replacing Lagrangian L with function f(L) for free particle
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