Action Definition: Integral of Lagrangian Over Time

[o_neg]

Hi,

why is the action defined as the integral of the Lagrangian over time?
i don't see the meaning of integral on the (kinetic - potential) energy

thanks,
ori.

 

[Meir Achuz]

The integral has no meaning by itself, but setting its variation equal to zero leads to the equations of motion.

 

[phreak]

You can see the integral as a way of measuring how much of something is used. So in this case, the integral measures how much (K-U) energy is being used up, and the path that a particle takes minimizes this (this isn't technically correct... it takes a 'stationary' path, but looking at it this way could be beneficial to the student visually).

 

[o_neg]

thanks for the replay.

I found a detailed explanation in the Feynman lectures on physics vol 2