All Questions
239
questions
7
votes
1
answer
2k
views
Principle of Least Action [duplicate]
Is the principle of least action actually a principle of least action or just one of stationary action? I think I read in Landau/Lifschitz that there are some examples where the action of an actual ...
- 1,880
23
votes
3
answers
2k
views
What makes a Lagrangian a Lagrangian?
I just wanted to know what the characteristic property of a Lagrangian is?
How do you see without referring to Newtonian Mechanics that it has to be $L=T-V$?
People constructed a Lagrangian in ...
- 1,880
6
votes
3
answers
1k
views
Principle of Least Action via Finite-Difference Method
I am reading Gelfand's Calculus of Variations & mathematically everything makes sense to me, it makes perfect sense to me to set up the mathematics of extremization of functionals & show that ...
- 4,101
5
votes
2
answers
523
views
Non-local Lagrangian contact interaction
Conside a contact interaction given by a delta function on their worldlines. Use a gauge fixed Lagrangian for two point particles in terms of their proper times $t$ and $t^{\prime}$. Is it possible to ...
- 3,206
6
votes
2
answers
665
views
Virtual differentials approach to Euler-Lagrange equation - necessary?
I'm currently teaching myself intermediate mechanics & am really struggling with the d'Alembert-based virtual differentials derivation for the Euler-Lagrange equation. The whole notion of, and ...
- 61
1
vote
1
answer
820
views
What's the motivation behind the action principle? [closed]
What's the motivation behind the action principle?
Why does the action principle lead to Newtonian law?
If Newton's law of motion is more fundamental so why doesn't one derive Lagrangians and ...
- 105
48
votes
5
answers
4k
views
Is the principle of least action a boundary value or initial condition problem?
Here is a question that's been bothering me since I was a sophomore in university, and should have probably asked before graduating:
In analytic (Lagrangian) mechanics, the derivation of the Euler-...
- 1,350
4
votes
2
answers
2k
views
What is the significance of action?
What is the physical interpretation of
$$ \int_{t_1}^{t_2} (T -V) dt $$
where, $T$ is Kinetic Energy and $V$ is potential energy.
How does it give trajectory?
- 185
16
votes
5
answers
6k
views
Why can't any term which is added to the Lagrangian be written as a total derivative (or divergence)?
All right, I know there must be an elementary proof of this, but I am not sure why I never came across it before.
Adding a total time derivative to the Lagrangian (or a 4D divergence of some 4 ...
- 1,263
31
votes
4
answers
6k
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 ...
- 955
130
votes
10
answers
41k
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 ...
- 8,540
7
votes
1
answer
2k
views
What variables does the action $S$ depend on?
Action is defined as,
$$S ~=~ \int L(q, q', t) dt,$$
but my question is what variables does $S$ depend on?
Is $S = S(q, t)$ or $S = S(q, q', t)$ where $q' := \frac{dq}{dt}$?
In Wikipedia I've ...
- 173
2
votes
1
answer
1k
views
Does Action in Classical Mechanics have a Interpretation? [duplicate]
Possible Duplicate:
Hamilton's Principle
The Lagrangian formulation of Classical Mechanics seem to suggest strongly that "action" is more than a mathematical trick. I suspect strongly that it ...
- 139
148
votes
8
answers
18k
views
Calculus of variations -- how does it make sense to vary the position and the velocity independently?
In the calculus of variations, particularly Lagrangian mechanics, people often say we vary the position and the velocity independently. But velocity is the derivative of position, so how can you treat ...
- 2,155