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September 15th, 2017, 06:33 AM  #1 
Newbie Joined: Sep 2017 From: Italy Posts: 1 Thanks: 0  Deducing Lagrangian of a system of free particles
Dear All, In Landau  Vol.1 (Mechanics)  Chapter 1  Paragraph 4 there is the passages to obtain Lagrangian of a system of free particles. From the chapter before it was deduced that: L = L(v^2), that is Lagrangian is only function of v^2 Than consider a new reference system with in which velocity of particle is: v' = v + epsilon so v'^2 = v^2 + 2v*eps + eps^2 so L(v'^2) = L(v^2 + 2v*eps + eps^2) Then he said: "Expanding this expression in power of epsilon and neglecting terms above the first order, we obtain:" L(v'^2) = L(v^2) + [partial_d (L) / partial_d (v^2)] * 2 * v * epsilon Please could you kindly illustrate the passages to reach this result? Thank you Vincenzo Last edited by greg1313; September 15th, 2017 at 02:08 PM. 

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deducin, deducing, free, lagrangian, particles, system 
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