Linked Questions

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0answers
441 views

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 ...
2
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0answers
394 views

Proof of Hamilton's principle [duplicate]

Is there a anything like a proof of Hamilton's principle? Where would I find it?
1
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1answer
285 views

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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1answer
122 views

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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0answers
255 views

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 ...
0
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0answers
234 views

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 ...
5
votes
1answer
96 views

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. ...
0
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0answers
127 views

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 ...
2
votes
1answer
44 views

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 ...
0
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0answers
42 views

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 ...
0
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0answers
26 views

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 ...
52
votes
7answers
52k views

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 ...
44
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6answers
9k views

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 ...
37
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3answers
3k views

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 ...
21
votes
5answers
4k views

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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