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### How do you determine the Lagrangian? [duplicate]

I have always been puzzled by how do you arrive at Lagrangians? That is, how do you know that the functional you need to get Newton's equations is $$L = T-V(x)~?$$ Do you derive the Lagrangian ...
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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 is the Lagrangian defined as $L=T - V$? [duplicate]

Please try to provide a sufficient answer, and when it is just „because it satisfies Newton‘s equations“, please try to give an example or explain it. If you know it, I would be very happy if you ...
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### Reason behind $L = T - V$ (Lagrangian formalism) [duplicate]

I've been learning about the Lagrangian formulation recently, and while I'm with the process, I am still struggling somewhat with the theory behind it. As I (rather poorly) understand it, the ...
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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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### Origin of Hamilton's variational principle [duplicate]

My question is what is the theoretical origin of Hamilton's principle. I mean is there any rigorous mathematical proof of this principle from some more basic principles?
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### How Lagrangian equations of motions can be obtained from Newton's laws? [duplicate]

Let's consider a system of $N$ point particles. Let's also assume that acceleration of each particle is a function of positions of all the particles. I assume that for such a system we can prove that ...
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If we start from $m\ddot{x} = -\frac{dV}{dx}$ How could one derive/construct principle of least action? i.e. find out that this quantity $S = \int_{t_0}^{t_1}dt\left(\frac{m\dot{x}^2}{2} - V(x) \... 14answers 9k views ### Lagrangians not of the form$T-U$My Physics teacher was reluctant to define Lagrangian as Kinetic Energy minus Potential Energy because he said that there were cases where a system's Lagrangian did not take this form. Are you are ... 10answers 28k views ### Why the Principle of Least Action? I'll be generous and say it might be reasonable to assume that nature would tend to minimize, or maybe even maximize, the integral over time of$T-V$. Okay, fine. You write down the action ... 6answers 14k views ### Hamilton's Principle Hamilton's principle states that a dynamic system always follows a path such that its action integral is stationary (that is, maximum or minimum). Why should the action integral be stationary? On ... 4answers 4k views ### Why can't we ascribe a (possibly velocity dependent) potential to a dissipative force? Sorry if this is a silly question but I cant get my head around it. 6answers 6k views ### Motivation for form of Lagrangian This question (in lagrangian mechanics) might be silly, but why is the Lagrangian L defined as:$L = T - V$? I understand that the total mechanical energy of an isolated system is conserved, and that ... 2answers 1k views ### Lagrangian Mechanics - Commutativity Rule$\frac{d}{dt}\delta q=\delta \frac{dq}{dt} \$

I am reading about Lagrangian mechanics. At some point the difference between the temporal derivative of a variation and variation of the temporal derivative is discussed. The fact that the two are ...
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### Are there examples in classical mechanics where D'Alembert's principle fails?

D'Alembert's principle suggests that the work done by the internal forces for a virtual displacement of a mechanical system in harmony with the constraints is zero. This is obviously true for the ...

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