All Questions
43
questions
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
36
votes
3
answers
25k
views
Deriving the Lagrangian for a free particle
I'm a newbie in physics. Sorry, if the following questions are dumb. I began reading "Mechanics" by Landau and Lifshitz recently and hit a few roadblocks right away.
Proving that a free ...
- 463
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
24
votes
4
answers
4k
views
Confusion regarding the principle of least action in Landau & Lifshitz "The Classical Theory of Fields"
Edit: The previous title didn't really ask the same thing as the question (sorry about that), so I've changed it. To clarify, I understand that the action isn't always a minimum. My questions are in ...
- 28.3k
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
16
votes
3
answers
6k
views
Hamilton-Jacobi Equation
In the Hamilton-Jacobi equation, we take the partial time derivative of the action. But the action comes from integrating the Lagrangian over time, so time seems to just be a dummy variable here and ...
- 921
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
7
votes
1
answer
3k
views
Proof that total derivative is the only function that can be added to Lagrangian without changing the EOM
So I was reading this: Invariance of Lagrange on addition of total time derivative of a function of coordiantes and time and while the answers for the first question are good, nobody gave much ...
- 560
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
9
votes
2
answers
1k
views
Does Newtonian $F=ma$ imply the least action principle in mechanics?
I've learned that Newtonian mechanics and Lagrangian mechanics are equivalent, and Newtonian mechanics can be deduced from the least action principle.
Could the least action principle $\min\int L(t,...
- 417
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
16
votes
7
answers
4k
views
In the Principle of Least Action, how does a particle know where it will be in the future?
In his book on Classical Mechanics, Prof. Feynman asserts that it just does. But if this is really what happens (& if the Principle of Least Action is more fundamental than Newton's Laws), then ...
- 504
10
votes
2
answers
4k
views
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
6
votes
1
answer
1k
views
Momentum as derivative of on-shell action
In Landau & Lifshitz' book, I got stuck into this claim that the momentum is the derivative of the action as a function of coordinates i.e.
$$
\begin{equation}p_i = \frac{\partial S}{\partial x_i}\...
- 430