I’m not very good with english, it isn’t my native language...., but I’m going to explain my question....(adsbygoogle = window.adsbygoogle || []).push({});

I’m reading the first book of Landau's series ,it’s about clasical mechanics.

In the second chapter you can find a problem about the conservation's theorem

the problem says The first problem says:

Find the ratio of the times in the same path for particles having different masses but the same potential energy.

the solution is: t'/t=sqrt(m'/m)

My tentative solution is supposing that the lagrangian for both paths are the same...

then:

L'=L

1/2m'v'^{2}-U=1/2mv^{2}-U

Finally:

t'/t=sqrt(m'/m)

BUT, It’s that correct?

and why the lagrangians are the same??? I’m not sure about the real concept (or meaning) of the lagrangian of a system...

thanks...

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# When the Lagrangians are equals?

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