52 questions linked to/from Why the Principle of Least Action?
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### How principle of least action? [duplicate]

I had learned the principle of least action.But I didn't get the motive behind taking the least action. Or why should the particle follow a path where it have a least action?
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### Why must the action be minimized? [duplicate]

In mechanics, the only physical route a particle can take is the one where action is minimized. Why is this true? Is there a proof?
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### What is the reason behind the stationarity of action? [duplicate]

I am reading Goldstein right now to understand the least action principle. I understood that the action needs to be stationary under small variation and this specifies the equation of motion, but do ...
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### Why should an action integral be stationary? On what basis did Hamilton state this principle?

Hamilton's principle states that a dynamic system always follows a path such that its action integral is stationary (that is, maximum or minimum). Why should the action integral be stationary? On ...
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### What is the difference between Newtonian and Lagrangian mechanics in a nutshell?

What is Lagrangian mechanics, and what's the difference compared to Newtonian mechanics? I'm a mathematician/computer scientist, not a physicist, so I'm kind of looking for something like the ...
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### Is there a proof from the first principle that the Lagrangian L = T - V?

Is there a proof from the first principle that for the Lagrangian $L$, $$L = T\text{(kinetic energy)} - V\text{(potential energy)}$$ in classical mechanics? Assume that Cartesian coordinates are ...
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### How general is the Lagrangian quantization approach to field theory?

It is an usual practice that any quantum field theory starts with a suitable Lagrangian density. It has been proved enormously successful. I understand, it automatically ensures valuable symmetries of ...
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### Motivation for form of Lagrangian

This question (in lagrangian mechanics) might be silly, but why is the Lagrangian L defined as: $L = T - V$? I understand that the total mechanical energy of an isolated system is conserved, and that ...
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### How do I show that there exists variational/action principle for a given classical system?

We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's ...
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### Advantages of Lagrangian Mechanics over Newtonian Mechanics [closed]

Here, I'm going to pose a very serious list of doubts I have on Lagrangian Mechanics. Can we learn Lagrangian Mechanics without studying Newtonian Mechanics? Does Lagrangian help in solving problems ...
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### In the Principle of Least Action, how does a particle know where it will be in the future?

In his book on Classical Mechanics, Prof. Feynman asserts that it just does. But if this is really what happens (& if the Principle of Least Action is more fundamental than Newton's Laws), then ...
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### Can you explain Fermat's Principle to me?

The textbook(F.A.Jenkins and H.E.White Fundamentals of Optics) states that the Fermat's principle is that the path taken by a light ray in going from one point to another through any set of media ...