All Questions
11
questions with no upvoted or accepted answers
4
votes
0
answers
170
views
Noether's Theorem in non-conservative systems
In most books on classical mechanics, Noether's Theorem is only formulated in conservative systems with an action principle. Therefore I was wondering if it is possible to also do that in non-...
- 470
2
votes
1
answer
72
views
Some doubts about action symmetry
We know that Symmetry of the Lagrangian ($\delta L = 0$) always yields some conservation law.
Now, if $\delta L \neq 0$, that doesn't mean we won't have conservation law, because if we can show action ...
- 525
2
votes
0
answers
76
views
Conflict of domain and endpoints in Noether's theorem and energy conservation
In the derivation of energy conservation, there is the transformation $q(t)\rightarrow q'(t)=q(t+\epsilon)$, whose end points are kind of fuzzy. The original path $q(t)$ is only defined from $t_1$ to $...
2
votes
0
answers
186
views
Conserved quantities of a simple Lagrangian
Suppose the following Lagrangian with 2 degrees of freedom:
$$L = \frac{3}{2}\dot{q}^2_{1} \ + \frac{3}{2}\dot{q}^2_{2} \ + \dot{q}_{1}\dot{q}_{2}$$
My aim is to find all the conserved quantities of ...
1
vote
0
answers
54
views
Doubt Regarding Noether's theorem for time-dependent systems
I'm having problems showing Noether's theorem when the lagrangian is time dependent. I'm trying to do it not using infinitesimal transformations from the beginning, but continuous transformations of a ...
1
vote
0
answers
70
views
Symmetry of a time-dependent Lagrangian
How do I get the group of symmetries and the constant of motion of $L=\frac{\dot{x}^2}{2}m+V(x+ct)$ where c is a constant?
When I tried to solve it, it was to look for shifts in $x$ and $ct$ under ...
- 11
1
vote
1
answer
67
views
Noethers Symmetries for a system in different cases
If the lagrangian is
$$L=\frac{m}{2}\left( \dot x_1^2+ \dot x_2^2\right)−b(x_1−x_2)^2+a( \dot x_1x_2− \dot x_2x_1).$$
What are the Noether symmetries of the system and the corresponding conserved ...
- 21
0
votes
0
answers
71
views
Conservations for time or space translational invariance, why $\delta L\vert_{\text{time trans}}\neq 0$? but $\delta L\vert_{\text{space trans}}= 0$?
To summarize my question first,
Given a classical mechanics Lagrangian,
$L=L(x(t), \dot{x}(t); t)$,
Why the conservation law for time $t$-translational invariant system, under time variance $\delta ...
- 4,336
0
votes
0
answers
112
views
How conserved quantities lead to equations of motion in Lagrangian mechanics
In a classical mechanics exercise, we were asked to derive a system of ODEs from conserved quantities. As we know from Lagrangian mechanics, Euler-Lagrange equations lead to equations of motion.
I ...
- 297
-1
votes
0
answers
81
views
Is there a straightforward simplified proof of energy conservation from time translation symmetry?
Electric charge conservation is easily proven from electric potential gauge symmetry, as follows:
The potential energy of an electric charge is proportional to the electric potential at its location.
...
-1
votes
2
answers
624
views
Conservation theorem for cyclic coordinates in the Lagrangian
Suppose $q_1,q_2,...,q_j,..,q_n$ are the generalized coordinates of a system.
$q_j$ is not there in the Lagrangian (it is cyclic).
Then $\frac{\partial L}{\partial\dot q_j}=constant$
In Goldstein, it ...
- 293