My Math Forum (http://mymathforum.com/math-forums.php)
-   Physics (http://mymathforum.com/physics/)
-   -   Deducing Lagrangian of a system of free particles (http://mymathforum.com/physics/341841-deducing-lagrangian-system-free-particles.html)

 vincelost September 15th, 2017 05:33 AM

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

 All times are GMT -8. The time now is 08:49 PM.