All Questions
26
questions
1
vote
2
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69
views
Given the Lagrangian of a system, is there a way to extract the total energy?
If an object of mass $m$ is under the action of a conservative force and there are no constraints on the system, can $E=K+U$ be obtained? If yes, I am more interested if the answer could be ...
- 11
6
votes
2
answers
766
views
Deriving special relativity free particle Lagrangian using infinitesimal boost?
At the very beginning of Landau and Lifshitz Mechanics they derive the form of the Lagrangian for a free particle in Newtonian mechanics.
I want to see how to do the analogous derivation in special ...
- 866
4
votes
1
answer
386
views
Does the negative sign in the Lagrangian $L=T-V$ relate to the $(+,-,-,-)$ Minkowski signature of relativity?
I've read many derivations of the Euler-Lagrange equation, but this is more of a physics-philosophical point.
Kinetic energy $T$ involves time derivatives, while potential involves spatial location. ...
- 568
2
votes
1
answer
226
views
In classical mechanics, can the Lagrangian be thought of as a metric?
I know that there are some other discussions on this on physics stack exchange, but the other day I was playing with the expression for the Lagrangian and thinking about it's connection with ...
- 281
1
vote
1
answer
701
views
How to check if the relativistic Lagrangian of a free particle is Lorentz invariant?
I am struggling with a concept in Classical Mechanics/Special Relativity.
I want to find the relativistic Lagrangian of a free particle, the method for which I have found in a few dfferent places, ...
- 11
3
votes
0
answers
141
views
Relativistic configuration space in classical mechanics
Okay so a couple of questions. Firstly I realise that in order to study the dynamics of one particle (classically), we define the Lagrangian and Hamiltonian to be the maps from the tangent and ...
- 504
2
votes
1
answer
3k
views
What is a Lagrangian of a photon? [duplicate]
In sense of classical mechanics+special relativity what is lagrangian of a photon?
Lagrangian of a relativistic massive particle is as follows:
$$ L_{massive}= -mc\sqrt{c^2-v^2} $$
So is it a zero?
- 529
4
votes
2
answers
2k
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Why do we consider Lagrangian densities in field theory (as opposed to Lagrangians as in point mechanics)?
My question is: Why do we consider Lagrangian densities in field theory (as opposed to Lagrangians as in point mechanics)?
Is it simply because of the following?
We wish the theories to be Lorentz ...
- 3,063
2
votes
2
answers
2k
views
Lagrangian for free particle in special relativity
From definition of Lagrangian: $L = T - U$. As I understand for free particle ($U = 0$) one should write $L = T$.
In special relativity we want Lorentz-invariant action thus we define free-particle ...
- 171
10
votes
2
answers
4k
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Deriving the action and the Lagrangian for a free massive point particle in Special Relativity
My question relates to
Landau & Lifshitz, Classical Theory of Field, Chapter 2: Relativistic Mechanics, Paragraph 8: The principle of least action.
As stated there, to determine the action ...
- 737
4
votes
2
answers
213
views
Does locality emerge from (classical) Lagrangian mechanics?
Consider a (classical) system of several interacting particles. Can it be shown that, if the Lagrangian of such a system is Lorenz invariant, there cannot be any space-like influences between the ...
- 34.4k