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I'm reading Landau/Lifchitz's mechanics book.

At equation (2.8), the author explains that when I add a time derivative of any function of time and coordinates f(q,t) to the lagrangian, the equations of motion are unchanged.

I understand the mathematical development leading to S' = S + f(q(2),t_2) + f(q(1),t_1), but I can't see why the equations of motion don't change.

I've tried to substitude the lagrangian of equation (2.8) in the Euler-Lagrange equations to convince myself it works, but that doesn't seem to be a good idea.

If you don't have this book and can't see what I'm talking about, I can provide you with more details.

Thank you !

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# Action and equations of motion

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