Linked Questions

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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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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, ...
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2answers
134 views

The action of a physical system

My knowledge in this topic is as follows, correct me if I'm wrong.: the action $S$ of a physical system is quantity such that the system evolves so that it's extemized, maximized or minimized, usually ...
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1answer
104 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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0answers
38 views

Why does nature favour systems that follow from a variational principle? [closed]

When Newton discovered ‘Newton’s law’ he was probably not aware that it could be viewed as a consequence of minimizing an ‘action integral’ (integral of some Lagrangian density). Since the same is ...
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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?
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1answer
173 views

Is there a "geometrical" reason for the principle of stationary action?

The principle of stationary action states that the trajectory $q(t)$ a physical system traces in configuration space is the one for which the action $$S[q]:=\int_{t_0}^{t_1}L(t,q,\dot q)\mathrm dt$$ ...
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3answers
491 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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2answers
151 views

How is Lagrangian mechanics a generalised version of Newton's laws?

I'm talking about the mechanics which uses the minimisation of integral of $L=T-V$ to deduce motion paths. I've read it is a more generalised version of Newton's formulation because it can be used ...
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1answer
221 views

Is there anything natural about the principle of "stationary action"?

In Taylor's classical mechanics, he derived Lagrange equations and showed that they are equivalent to Newton's second law. Then, it was obvious that Lagrange equations are similar to the Euler-...
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2answers
168 views

Assumptions reg. Kinetic energy and Potential energy in the Lagrangian formulation

I have recently been introduced to Lagrangian mechanics. My previous exposure to Lagrangian math has been in the form of optimizing constrained functions using Lagrange multipliers. I get the math ...
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4answers
269 views

Deeper Meaning to the Nature of Lagrangian

Is there a more fundamental reason for the Classical Lagrangian to be $T-V$ and Electromagnetic Lagrangian to be $T-V+ qA.v$ or is it simply because we can derive Newton's Second Law and Lorentz Force ...
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88 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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1answer
140 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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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?

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