52 questions linked to/from Why the Principle of Least Action?
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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 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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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}... 1answer 67 views ### Least action principle universality, why does it work? [duplicate] For example, hen working with general relativity, one sees that Einstein equations can be derived from an action principle via the Einstein-Hilbert action. This occurs too in classical mechanics, ... 1answer 61 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 ... 0answers 43 views ### 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? 0answers 32 views ### 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? 0answers 26 views ### 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 ... 7answers 17k views ### 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 ... 7answers 69k 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 ... 7answers 7k 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 ... 3answers 4k 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 ... 6answers 8k views ### 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 ... 3answers 4k views ### 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 ... 3answers 19k views ### 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 ... 6answers 2k views ### 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 ... 4answers 5k views ### 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 ... 2answers 775 views ### Does Newtonian$F=ma$imply the least action principle in mechanics? I've learned that Newtonian mechanics and Lagrangian mechanics are equivalent, and Newtonian mechanics can be deduced from the least action principle. Could the least action principle$\min\int L(t,...
I suspect this has been asked here before, but I didn't find anything using Search. Why is Newton's second law only second-order in position? For instance, could there exist higher-order masses $m_i$ ...