(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Demonstrate that if the Lagrangians [tex]L(q, \dot q ,t)[/tex] and [tex]L'(q, \dot q , t)[/tex] who differ in a total derivative of a function f(q,t) give the same motion equations.

That is, [tex]L'=L +\frac{d}{dt}f(q,t)[/tex]

2. Relevant equations

Euler-Lagrange's equation.

3. The attempt at a solution

I tried to use Euler-Lagrange's equation to see if I could reach the same equations for L and L' but without any success. I've checked out in Landau & Lifgarbagez's book. Here is what it more or less says: "If we have [tex]L'=L+\frac{d}{dt}(2a \vec r \cdot \dot \vec r+a \dot r ^2 t)[/tex], we can omit the second term since it's a total derivative with respect to time."

So according to this book it's obvious while I have to prove it. But I don't understand why it's obvious nor why it's true.

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# Homework Help: Difference between 2 Langrangians, proof

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