Invariance of lagrangian with $\frac{d}{dt}(f(q,t))$

Asked Dec 27 '16 at 11:17

Active Dec 27 '16 at 11:19

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I know that if we have a lagrangian such that

$$ L'=L+\frac{d}{dt}(f(q,t))$$ then the equation of motion will be the same for $L$ or $L'$.

But I would like to know if there is a proof of the opposite, ie :

If $L$ and $L'$ describe the same motion, then $$ L'=L+\frac{d}{dt}(f(q,t))$$

I don't know how to prove it?

edited Dec 27 '16 at 11:19

asked Dec 27 '16 at 11:17

StarBucK

1

Related: http://physics.stackexchange.com/q/174137/2451 , http://physics.stackexchange.com/q/87628/2451 and links therein. – Qmechanic Dec 27 '16 at 11:19
They proove that IF L'=L+d/dt (f) THEN the equation of motion will be the same.
I am asking if there is a proof of : IF L and L' describe same motion, THEN L'=L+d/dt f
– StarBucK Dec 27 '16 at 11:31
1

Possible duplicate: http://physics.stackexchange.com/q/131925/2451 – Qmechanic Dec 27 '16 at 11:36
Thank you.
So there is no proof of the opposite as we also can do a dilatation of our lagrangian without changing the dynamic
– StarBucK Dec 27 '16 at 12:38
$\uparrow$ Yes. – Qmechanic Dec 27 '16 at 15:20

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