Linked Questions

2 votes
0 answers
1k views

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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0 votes
3 answers
694 views

How is Lagrangian Mechanics useful? [duplicate]

I recently started reading about Lagrangian Mechanics. I observed that it uses some basic expressions that are derived by taking Newton's laws of motion as fundamental such as kinetic energy, ...
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2 votes
0 answers
608 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 ...
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  • 1,383
-2 votes
1 answer
357 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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7 votes
1 answer
224 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. ...
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1 vote
1 answer
303 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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0 votes
0 answers
283 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 ...
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0 votes
0 answers
269 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 ...
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0 votes
0 answers
267 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 ...
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0 votes
0 answers
216 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 ...
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3 votes
1 answer
162 views

Why is there a Lagrangian? [duplicate]

In all discussions regarding the Lagrangian formulation it has always been said that $L = T - V $, only is a correct guess that when operated via through the Euler -Lagrange equation yields something ...
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0 votes
2 answers
83 views

How does nature know Hamilton's principle? [duplicate]

I have gone through some of the questions asked here re Hamilton's principle, but could not readily find an answer to the following: Hamilton's principle states that paths particles follow extremizes ...
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2 votes
1 answer
127 views

Why does it seem like there is always a Lagrangian? [duplicate]

All the fundamental laws of physics can be written in terms of an action principle. This includes electromagnetism, general relativity, the standard model of particle physics, and attempts to go ...
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-2 votes
1 answer
95 views

Why principle of least action is true? [duplicate]

Recently I am studying lagrangian mechanics where I came across the topic "principle of least action" which states that a system always takes the path of least action or when the action is ...
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1 vote
0 answers
93 views

Why does the action $S=\int L dt=\int (T-V) dt$ have to be minimised (or maximised) to produce Newton's Second Law? [duplicate]

We have recently covered the Lagrangian in our lectures, whereby it was shown that all equations of motion ($x(t)$) satisfying the Euler-Lagrange equation with Lagrangian $L=T-V$, where $T=\frac{1}{2}...
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