A Lagrangian: kinetic matrix Z_ij and mass matrix k_ij

AI Thread Summary
The discussion revolves around the diagonal nature of the kinetic term for fluctuations in Lagrangian mechanics and the addition of the square root of mass for normalization. Participants express confusion about the significance of Z_ij being equal to delta_ij and seek clarification on these concepts without specific context from the example referenced. The importance of citing the relevant textbook or paper for clarity is emphasized. Understanding these terms is crucial for grasping the underlying principles of the Lagrangian framework. Overall, the conversation highlights the need for clearer explanations in theoretical physics discussions.
GGGGc
Screen Shot 2023-10-04 at 08.43.45.png

Can somebody explain why the kinetic term for the fluctuations was already diagonal and why to normalize it, the sqrt(m) is added? Any why here Z_ij = delta_ij?
Quite confused about understanding this paragraph, can anybody explain it more easily?
 
Physics news on Phys.org
How can we answer this question, without knowing, what the example actually is? It's also mandatory to quote the textbook/paper you picture is taken from.
 

Thread 'The Effect of Linear and Rotational Motion on Measured Weight'

Consider an extremely long and perfectly calibrated scale. A car with a mass of 1000 kg is placed on it, and the scale registers this weight accurately. Now, suppose the car begins to move, reaching very high speeds. Neglecting air resistance and rolling friction, if the car attains, for example, a velocity of 500 km/h, will the scale still indicate a weight corresponding to 1000 kg, or will the measured value decrease as a result of the motion? In a second scenario, imagine a person with a...
View full post »

Thread 'Coulomb gauge implies instantaneous radial electric field?'

Scalar and vector potentials in Coulomb gauge Assume Coulomb gauge so that $$\nabla \cdot \mathbf{A}=0.\tag{1}$$ The scalar potential ##\phi## is described by Poisson's equation $$\nabla^2 \phi = -\frac{\rho}{\varepsilon_0}\tag{2}$$ which has the instantaneous general solution given by $$\phi(\mathbf{r},t)=\frac{1}{4\pi\varepsilon_0}\int \frac{\rho(\mathbf{r}',t)}{|\mathbf{r}-\mathbf{r}'|}d^3r'.\tag{3}$$ In Coulomb gauge the vector potential ##\mathbf{A}## is given by...
View full post »

Thread 'Simple thought experiment with Stefan-Boltzmann law: energy'

Dear all, in an encounter of an infamous claim by Gerlich and Tscheuschner that the Greenhouse effect is inconsistent with the 2nd law of thermodynamics I came to a simple thought experiment which I wanted to share with you to check my understanding and brush up my knowledge. The thought experiment I tried to calculate through is as follows. I have a sphere (1) with radius ##r##, acting like a black body at a temperature of exactly ##T_1 = 500 K##. With Stefan-Boltzmann you can calculate...
View full post »

Similar threads

I Why isn't the Lagrangian invariant under ##\theta## rotations?
Replies
5
Views
2K
I Motivation for mass term in Lagrangians
Replies
2
Views
3K
Looking for good books explaining Lagrangian and Hamiltonian Mechanics
Replies
28
Views
3K
I Normal modes of vibration from the total energy
Replies
3
Views
1K
A One Hamiltonian formalism query - source is Goldstein's book
Replies
1
Views
1K
A The Lagrangian a function of 'v' only and proving v is constant
Replies
3
Views
2K
Lagrangian without K.E and any anthromorophic answer
Replies
7
Views
2K
Stationary points classification using definiteness of the Lagrangian
Replies
4
Views
2K
Lagrangian of a double pendulum, finding kinetic energy
Replies
3
Views
3K
When the Lagrangians are equals?
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top