All Questions
237
questions
1
vote
2
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106
views
Does Hamilton's principle allow a path to have both a process of time forward evolution and a process of time backward evolution?
This is from Analytical Mechanics by Louis Hand et al. The proof is about Maupertuis' principle. The author seems to say that Hamilton's principle allow a path to have both a process of time forward ...
- 353
2
votes
0
answers
72
views
Why can't we treat the Lagrangian as a function of the generalized positions and momenta and vary that? [duplicate]
Some background: In Lagrangian mechanics, to obtain the EL equations, one varies the action (I will be dropping the time dependence since I don't think it's relevant) $$S[q^i(t)] = \int dt \, L(q^i, \...
- 93
7
votes
3
answers
2k
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Something fishy with canonical momentum fixed at boundary in classical action
There's something fishy that I don't get clearly with the action principle of classical mechanics, and the endpoints that need to be fixed (boundary conditions). Please, take note that I'm not ...
- 7,572
0
votes
1
answer
76
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In Lagrangian mechanics, do we need to filter out impossible solutions after solving?
The principle behind Lagrangian mechanics is that the true path is one that makes the action stationary. Of course, there are many absurd paths that are not physically realizable as paths. For ...
- 50.1k
0
votes
0
answers
88
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Deeper explanation for Principle of Stationary Action [duplicate]
The Principle of Stationary Action (sometimes called Principle of Least Action and other names) is successfully applied in a wide variety of fields in physics. It can often can be be used to derive ...
- 16.9k
-2
votes
1
answer
108
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Why the choice of Configuration Space in Hamilton's Principle is $(q, \dot{q}, t)$? [closed]
In most physics books I've read, such as Goldstein's Classical Mechanics, the explanation of Hamilton's principle took into consideration the equation (1) known as Action:
$$\displaystyle I = \int_{...
- 113
3
votes
3
answers
130
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Is there a proof that a physical system with a *stationary* action principle cannot always be modelled by a *least* action principle?
I'm aware that with Lagrangian mechanics, the path of the system is one that makes the action stationary. I've also read that its possible to find a choice of Lagrangian such that minimization is ...
- 50.1k
1
vote
1
answer
33
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Regarding varying the coefficients of constraints in the pre-extended Hamiltonian in Dirac method
consider the following variational principle:
when we vary $p$ and $q$ independently to find the equations of motion, why aren't we explicitly varying the Coeff $u$ which are clearly functions of $p$ ...
5
votes
3
answers
627
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Is Principle of Least Action a first principle? [closed]
It is on the basis of Principle of Least Action, that Lagrangian mechanics is built upon, and is responsible for light travelling in a straight line.
Is its the classical equivalent of Schrodinger's ...
0
votes
1
answer
58
views
Euler-Lagrange confusion
Consider the action $S = \int dt \sqrt{G_{ab}(q)\dot{q}^a\dot{q}^b}.$
Now for computing the Euler-Lagrange equations, we need the time derivative of $\frac{\partial L}{\partial \dot{q}^c} = \frac{1}{\...
- 298
2
votes
3
answers
148
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Derivation of Hamiltonian by constraining $L(q, v, t)$ with $v = \dot{q}$
I am trying to reconstruct a derivation that I encountered a while ago somewhere on the internet, in order to build some intuition both for $H$ and $L$ in classical mechanics, and for the operation of ...
- 23
0
votes
1
answer
78
views
Is $F=-\nabla V$ a form of the least action principle? [closed]
Only for conservative systems, of course.
0
votes
1
answer
94
views
Virtual work of constraints in Hamilton‘s principle
Goldstein 2ed pg 36
So in the case of holonomic constraints we can move back and forth between Hamilton's principle and Lagrange equations given as $$\frac{d}{d t}\left(\frac{\partial L}{\partial \...
- 1,260
3
votes
3
answers
785
views
Confusion of variable vs path in Euler-Lagrange equation, Hamiltonian mechanics, and Lagrangian mechanics
In Lagrangian mechanics we have the Euler-Lagrange equations, which are defined as
$$\frac{d}{dt}\Bigg(\frac{\partial L}{\partial \dot{q}_j}\Bigg) - \frac{\partial L}{\partial q_j} = 0,\quad j = 1, \...
- 3,350
2
votes
2
answers
153
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What is the most general transformation between Lagrangians which give the same equation of motion?
This question is made up from 5 (including the main titular question) very closely related questions, so I didn't bother to ask them as different/followup questions one after another. On trying to ...
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