All Questions
84
questions
0
votes
2
answers
49
views
How did the boundary term vanish in deriving equation of motion from Lagrangian? [closed]
I was deriving the equation of motion from Lagrangian, by using the principle of least action. Usually, at this point in derivation,
$$\int dt \frac{\partial L}{\partial \dot{q}} \frac{\partial}{\...
0
votes
1
answer
76
views
In Lagrangian mechanics, do we need to filter out impossible solutions after solving?
The principle behind Lagrangian mechanics is that the true path is one that makes the action stationary. Of course, there are many absurd paths that are not physically realizable as paths. For ...
- 50.1k
1
vote
0
answers
52
views
Units for the Calculus of Variations [duplicate]
Just a quick question regarding the units for a quantity. I just started reading a QFT textbook, and it starts out with a little bit of Calculus of Variations. Specifically, there is a result that ...
4
votes
4
answers
245
views
Variation of a function
I'm studying calculus of variations and Lagrangian mechanics and i don't understand something about the variational operator
Let's say for example that i got a Lagrangian $L [x(t), \dot{x}(t), t] $ ...
- 309
0
votes
0
answers
47
views
Equation of motion from lagrangian for an holonomic system with fixed constraints
We know that the lagrangian function of a holonomic system subject to fixed constraints has the form
$$\mathcal{L}(\mathbf{q,\dot{q}})=\frac{1}{2} \langle \mathbf{\dot{q},A(q)\dot{q}} \rangle - U(\...
2
votes
1
answer
175
views
Doubts about Noether's theorem derivation
Assume you have an action:
$S[q] = \int L(q, \dot q, t)$ (i.e $q$ is a function of time). (1) Then you do a transformation on $q(t)$ such as $\sigma(q(t), a)$ where $a$ is infinetisemal and this ...
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
$$\frac{d}{dt}\Bigg(\frac{\partial L}{\partial \dot{q}_j}\Bigg) - \frac{\partial L}{\partial q_j} = 0,\quad j = 1, \...
- 3,350
0
votes
1
answer
104
views
Classical Mechanics proof Lagrangian constraint forces
I've got a simple mathematical question. I was studying the Lagrangian approach of classical mechanics and in this part I had the intention of proving that the differential of the Lagrangian is equal ...
5
votes
1
answer
712
views
Confusion in derivation of Euler-Lagrange equations
Here's a screenshot of derivation of Euler-Lagrange from feynman lecture https://www.feynmanlectures.caltech.edu/II_19.html
My doubt is in the last paragraph. I get that $\eta = 0$ at both ends, but ...
- 301
0
votes
1
answer
148
views
How did Landau & Lifshitz (Mechanics) get Equation 2.5?
I understood everything in Landau & Lifshitz's mechanics book until Equation 2.4,but I'm not sure what he means when he says "effecting the variation" and gets Equation 2.5.
Can anyone ...
1
vote
1
answer
51
views
Lagrange momentum for position change
After the tremendous help from @hft on my previous question, after thinking, new question popped up.
I want to compare how things behave when we do: $\frac{\partial S}{\partial t_2}$ and $\frac{\...
- 525
1
vote
1
answer
81
views
On generalised potential in Electrodynamics
I'm studying Lagrangian Mechanics from Goldstein's Classical Mechanics. My question concerns Section 1.5 which talks about velocity-dependent potentials.
I am actually unsure about how Equation 1-64' ...
- 1,640
0
votes
4
answers
354
views
A step in the derivation of the Euler-Lagrange equations using Hamilton's Principle
I am going through the derivation of the Euler-Lagrange equations from Hamilton's principle following Landau and Lifshitz Volume 1. We start by writing the variation in the action as,
$$\delta S = \...
1
vote
3
answers
864
views
Deriving Hamilton's Principle from Lagrange's Equations
I'm trying to derive Hamilton's Principle from Lagrange's Equations, as I've heard they're logically equivalent statements, and am stuck on a final step. For simplicity, assume we're dealing with a ...
- 245
1
vote
1
answer
77
views
Virtual displacement in semi-holonomic constraints
I am currently studying Lagrangian Mechanics for systems whose constraints equations have the form $$\sum_{k=1}^na_{\ell k}(q,t)\dot{q}_k+a_{\ell t}(q,t)=0\tag{1}$$
or, equivalently
$$\sum_{k=1}^na_{\...
- 154