## Lagrangian's formalism and Fermat's principle

Based on Lagrangian's formalism one can write Eq.(2.9) as
 (2.10)

where represents the system's Lagrangian:
 (2.11)

Within the context of the formalism is supposed to be a function of coordinates and generalized velocities[5]:
 (2.12)

where

In this way, the perturbation of the travel time corresponds to

According to Fermat's principle

which implies that
 (2.13)

On the other side, using Eq.(2.12) one can obtain that

Therefore, one can conclude that the solution of the Eikonal equation requires the solution of the following system of equations:

 (2.14)

Orlando Camargo Rodríguez 2012-06-21