All Questions
16
questions with no upvoted or accepted answers
7
votes
0
answers
135
views
Variational principle with $\delta I \neq 0$
In Covariant Phase Space with Boundaries D. Harlow allows boundary terms in the variation of the action. If we have some action $I[\Phi]$ on some spacetime $M$ with boundary $\partial M = \Gamma \cup \...
- 36.4k
2
votes
0
answers
161
views
Problem understanding something from the variational principle for free particle motion (James Hartle's book, chapter 5)
I am currently studying general relativity from James Hartle's book and I have trouble understanding how he goes to equation (5.60) from equation (5.58). It's about the variational principle for free ...
2
votes
1
answer
109
views
How does derivation of Lagrange equation from d’Alembert principle differ from the derivation of it from principle of least action?
Using d’Alembert principle, one doesn't require any assumption like the one made in other case where particle has to follow the path of least action.
- 21
2
votes
1
answer
333
views
How do we get Maupertuis Principle from Hamilton's Principle?
Maupertuis principle says that if we know the initial and final coordinates but not time, the total energy and the fact that energy is conserved, we can choose the "right" path from all mathematically ...
2
votes
1
answer
265
views
Clarifications regarding the Maupertuis/Jacobi principle
I'm slightly confused regarding the Maupertuis' Principle. I have read the Wikipedia page but the confusion is even in that derivation. So, say we have a Lagrangian described by $\textbf{q}=(q^1,...q^...
- 353
2
votes
0
answers
270
views
Decoupling of generalized coordinates in lagrangian
Say you have a lagrangian $L$ for a system of 2 degrees of freedom. The action, S is:
$S[y,z] = \int_{t_1}^{t_2} L(t,y,y',z,z')\,dt \tag{1}$
If $y$ and $z$ are associated with two parts of the ...
- 1,222
1
vote
1
answer
87
views
Is Hamilton’s principle valid for systems that are not monogenic?
I have read in Goldstein that Hamilton’s principle works only for monogenic systems. Is it true? I thought that the action principle is universal?
1
vote
0
answers
70
views
Hamilton's principle for fields
According to Goldstein, Hamilton's principle can be summerized as follows:
The motion of the system from time $t_{1}$ to time $t_{2}$ is such that the line integral (called the action or the action ...
- 1,131
1
vote
1
answer
55
views
Is a trajectory connecting two points valid for all the intermediate points too?
Suppose a particle is described by a Lagrangian $\mathcal L(q_i, \dot{q_i}, t)$. Suppose that $q_i(t)$ is a trajectory (there might be more that one) along which the action integral is stationary for ...
- 1,951
1
vote
0
answers
30
views
Finding well-posed variational form for contour shape optimization
In a given physical problem near resonance, it is required that two energy terms, $\iint_{A} [f(x,y)]^{2}dxdy$ and $\iint_{A}[g(x,y)]^{2}dxdy$, in the system under consideration be almost equal. In ...
- 632
0
votes
1
answer
76
views
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 ...
- 50.2k
0
votes
1
answer
95
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 $$\frac{d}{d t}\left(\frac{\partial L}{\partial \...
- 1,270
0
votes
0
answers
34
views
Obtaining the critical solution for a functional
So, I was trying to calculate the critical solution $y = y(x)$ for the following functional:
$$J[y] = \int_{0}^{1} (y'^{\: 2} + y^2 + 2ye^x)dx$$
and a professor of mine said I should use conservation ...
0
votes
0
answers
37
views
The action principle is the statement about minimizing something around trajectory
I watched the special relativity lecture (4) for Prof. Susskind and about some last minutes of it, he said:
"The action principle is the statement about minimizing something around trajectory".
I ...
- 427
0
votes
0
answers
3k
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Simple real life applications of Euler-Lagrange equations of motion
If you read some introductory mechanics text like David Morin's Introduction to Classical Mechanics about Euler Lagrange Equations you get a large amount of simple examples like the "moving plane" (...
- 1,692