38 questions linked to/from Why the Principle of Least Action?
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### Why does Principle for least action hold for classical fields [duplicate]

Let $\mathscr L (\phi(\mathbf x), \partial \phi(\mathbf x))$ denote the Lagrangian density of field $\phi(\mathbf x)$. Then then actual value of the field $\phi(\mathbf x)$ can be computed from the ...
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### Proof of Hamilton's principle [duplicate]

Is there a anything like a proof of Hamilton's principle? Where would I find it?
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### Why do Lagrangians and Hamiltonians give the equations of motion? [duplicate]

I remember asking my second year Mechanics teacher about why do the Lagrangians give the equations of motion. His answer was that there is no answer to that, it is an empirical fact, and that asking ...
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### What is the principle of least action? [duplicate]

I want to understand the principal of least action intuitively, away from any mathematical proof.
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### Physical motivation for Lagrangian formalism [duplicate]

This is more of a request for clarification of understanding and intuition rather than a question, but I hope people can help me with it. I have learned calculus of variations and have subsequently ...
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### The principle of least action [duplicate]

I have read about the principle of least action. This principle suggests that nature would allow a particle to travel in a path along which the integral of the difference between kinetic energy and ...
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### Why are action principles so powerful and widely applicable? [duplicate]

I've been trying to wrap my head around Lagrangian mechanics and Lagrangians in general, and I've found it difficult. After some thinking, I believe that the issue I have is with action principles. ...
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### Is there any reason for principle of least action to be true? [duplicate]

My question is not rigidly related to physics. The principle of least actions says that for any dynamical system there exists a function parameterized by $q$'s and $\dot{q}$'s such that the line ...
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### How can the action can describe a movement? What is the argument behind? [duplicate]

We define the action of a system as $$S(q)=\int_{t_1}^{t_2}L(t,q(t),q'(t))dt,$$ where $q(t)$ is the evolution of the system and $L$ is the Lagrangien. How can a stationary point of $S$ can describe ...
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### Intuition behind the use of the Principle of Stationary Action in Classical Field Theory [duplicate]

Whilst studying Field Theory and after checking numerous sources it appears that people always just state the action without providing some sort of motivation/intuition as to why we should/can use the ...
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### How is the problem of finding an object's motion an functional extrema problem? [duplicate]

I'm learning about Lagrangian mechanics and I've learned about the Lagrangian. I've read a proof of the fact that if $$J = \int_a^b F(x,f(x),f'(x) dx .$$ Then the function $f(x)$ that extremizes ...
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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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### Hamilton's 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 ...
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 ...