Relationship between Lagrangian and Energy

AI Thread Summary
For time-independent potentials, the energy relationship is expressed as E = sum(Vi * partial dL/dVi) - L. When dealing with time-dependent potentials, the relationship modifies to total dE/dt = - partial dL/dt. This adjustment reflects the dynamics introduced by the time dependence of the potentials. A request for textbooks that derive this relationship was made, noting that "Mechanics" by Landau and Lifgarbagez does not cover it. The discussion emphasizes the need for resources that address energy and Lagrangian dynamics in the context of time-dependent systems.
theneedtoknow
Messages
169
Reaction score
0
I know that, for time-independent potentials, we have E=sum (Vi*partial dL/dVi) - L
What if one or more of the potentials are time-dependent?
Is the relationship between energy and the lagrangian then "total dE/dt = - partial dL/dt "?
 
Physics news on Phys.org
Thank you! Would you happen to know of any textbooks where this is derived? I have the Landau and Lifgarbagez "Mechanics" one and they do not do so.
 
Thread 'Gauss' law seems to imply instantaneous electric field'

Thread 'Gauss' law seems to imply instantaneous electric field'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
View full post »

Thread 'Highway: Deriving speed from Doppler shift'

I passed a motorcycle on the highway going the opposite direction. I know I was doing 125/km/h. I estimated that the frequency of his motor dropped by an entire octave, so that's a doubling of the wavelength. My intuition is telling me that's extremely unlikely. I can't actually calculate how fast he was going with just that information, can I? It seems to me, I have to know the absolute frequency of one of those tones, either shifted up or down or unshifted, yes? I tried to mimic the...
View full post »

Similar threads

I Mathematical proof for the Lagrangian function
Replies
4
Views
1K
I Lagrangian doesn't change when adding total time derivative
Replies
19
Views
3K
I Lagrangian for pendulum
Replies
11
Views
2K
A Treating Velocity as Independent of position till the end in Lagrangian Mechanics
Replies
6
Views
2K
I Lagrangian density of a linearly elastic string under gravity
Replies
6
Views
1K
A Lagrangian to the Euler-Lagrange equation
Replies
1
Views
2K
I Taylor expansion about lagrangian in noether
Replies
1
Views
1K
I Landau's inertial frame logic
Replies
1
Views
1K
I Missing exponent in "Theoretical Minimum"?
Replies
4
Views
1K
I Momentum and Action: Understanding Lagrangian Mechanics
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top