# What's the motivation behind the action principle? [closed]

1. What's the motivation behind the action principle?

2. Why does the action principle lead to Newtonian law?

3. If Newton's law of motion is more fundamental so why doesn't one derive Lagrangians and Hamilton principle from it?

4. Also does all Lagrangians obey $L=T-V$?

5. I think that it's related to the fact that the kinetic energy of the particle at all points on the path or it's travel time is as small as possible?

6. If so, How can we derive the principle of least action from this fact in detail?

• Possible duplicates: physics.stackexchange.com/q/9/2451 and links therein. Nov 24 '12 at 10:58
• Welcome to physics.SE. I'm closing this not because it is a bad question but because it is a list of questions and that rather breaks the model we use here. Further several of the questions you ask have already been answered on the site. In particular we have addressed both the matter of getting to Lagrangian and Hamiltonian mechanics from Newtonian mechanics (you can and it was first done that way, the action principle came later) and the rather subjective one of "fundemental"-ness. Nov 24 '12 at 17:19

4. No. This is only the form of Lagrangians for $n$-particle systems in Cartesian coordinates - the stuff with which one begins in theoretical mechanics.