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## Homework Statement

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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.

## Homework Equations

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Euler-Lagrange equations.

## The Attempt at a Solution

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?