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  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?

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closed as not a real question by Qmechanic, Manishearth, dmckee Nov 24 '12 at 17:16

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

    
Possible duplicates: physics.stackexchange.com/q/9/2451 and links therein. –  Qmechanic Nov 24 '12 at 10:58
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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. –  dmckee Nov 24 '12 at 17:19
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1 Answer 1

  1. The motivation is that it works. It was a major discovery that this unifies mechanics (in the absence of friction).

  2. It doesn't lead to newton's law, as it is far mor general than the latter, but applied to the problems Newton was interested, it implies these laws.

  3. Action is more fundamental than newton's laws. The latter are more intutive, though, hence were found much earlier in history and can be taught much earlier in education.

  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.

  5. What is related? Minimal travel time is a vartiational principle different from the action principle and gives the same answers only in very special cases.

  6. is not applicable.

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