Motion in a non-inertial frame

[Andrea Vironda]

Hi,
in this Landau's extract i note that the total derivative is neglected in 2 places.
in the first case i think because it's raised twice, but in the second case?

 

[Orodruin]

A total derivative in the Lagrangian does not affect the equations of motion as it only contributes with a boundary term.

 

[Andrea Vironda]

a boundary term.

sorry for my english, but what is that?

 

[Orodruin]

A contribution from the boundary that remains after integration. Think divergence theorem where the integral total derivative $\nabla\cdot \vec v$ is rewritten as a surface integral over the boundary of the original integration volume.