Linked Questions

7
votes
1answer
2k views

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 ...
0
votes
0answers
261 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 ...
0
votes
1answer
105 views

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 ...
1
vote
0answers
99 views

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 ...
2
votes
1answer
53 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 ...
1
vote
0answers
49 views

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?
0
votes
0answers
37 views

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 ...
1
vote
0answers
28 views

Is there a way to derive Principle of Least Action from Newton's laws instead of other ways around? [duplicate]

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) \...
71
votes
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 ...
92
votes
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 ...
51
votes
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 ...
18
votes
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.
12
votes
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 ...
24
votes
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 ...
24
votes
2answers
5k views

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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