| Ok, I'll tell you what. Let's leave this 1905 business aside for a 
| moment and consider something much older, let's say from the 1700s. 
| Write down the Lagrangian for a free particle in 3D space, in Cartesian 
| coordinates, unconstrained except for earth's gravity. Write the 
| equation of motion resulting from this. 
| 
| As a hint: this is an *unbelievably* easy exercise that takes about 4 
| short lines to write down. Not only I did not put any constraints, I 
| even allowed you the luxury of Cartesian coordinates. I'm just curious 
| how much physics you know. 

Are you really? 
In that case.... wonder. 
But here's a hint. 
  http://www.physics.montana.edu/faculty/cornish/lagrange.gif