All Questions
Tagged with lagrangian-formalism homework-and-exercises
979
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Centrifugal Governor Question [closed]
I've been working through Hand and Finch's Analytical Mechanics and have just attempted this question:
My attempt at a solution is as follows:
First, find the kinetic energy of the two masses $m$ by ...
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Find curve minimizing energy loss due to friction [closed]
I am looking for an ansatz of the following problem:
Given a mass $m$ moving in a constant gravitational field along curves $C$ connecting two fixed points I want to find the curve $C_0$ that ...
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Action-angle variables for three-dimensional harmonic oscillator using cylindrical coordinates
I am solving problem 19 of ch 10 of Goldstein mechanics. The problem is:
A three-dimensional harmonic oscillator has the force constant k1 in the x- and y- directions and k3 in the z-direction. Using ...
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How to do Variational Principle in QFT? ($SU(2)$-Yang-Mills)
I am currently familiarizing myself with QFT and have a question about this article. My understanding is that the Lagrangian density in (2) couples my gauge fields to the Higgs field. And with ...
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Equation of motion of free field Lagrangian
I tried to derive the equation of motion obtained by varying Lagrangian (2) in https://arxiv.org/abs/0804.4291 wrt the metric. It is supposed to give the second equation in (5) of the paper but my ...
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Spring hanging on a spinning Disk
I have already asked a question on the Math stack-exchange.
You can find it under the following link:
https://math.stackexchange.com/q/4876146/
I felt like the question is better suited for this stack-...
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Finding the Noether current
I'm currently reading "QFT for the gifted Amateur by Lancaster and Blundell, and in a lot of the problems I'm a bit unsure of how to do them, an example asked
"Consider a system ...
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Noether current for Yang-Mills theory in the absence of scalar field
The theory with an arbitrary compact gauge group $G$ is given. And global transformations are valid (see below)
$$
A_{\mu}\mapsto{A^{'}_{\mu}={\omega}A_{\mu}\omega^{-1}}
$$
also $\omega \in G$ and it ...
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Using functional derivatives and Euler-Lagrange to obtain wave equation in 3d elastic media
I'm trying to solve exercise (1.5) from Lancaster and Blundell's Quantum Field Theory for the Gifted Amateur wherein we consider a 3D elastic material whose potential energy is given by
$$ V = \frac{\...
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Where am I going wrong when obtaining the Hamiltonian density for the electromagnetic field?
I'm trying to verify that the Hamiltonian density for the classical electromagnetic field is equal to the energy density. But the electric field is disappearing and only the energy density of the ...
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Variation of the Einstein-Hilbert action to derive the metricity condition
Consider the Einstein-Hilbert action: $$S=\int d^{4} x \sqrt{-g} g^{\mu \nu} R_{\mu \nu}$$
If we vary it with respect to the connection, assuming no prior relation between the metric and the ...
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Question about Problem $12$ in Chapter $11$ from Kibble & Berkshire's book
I write again the problem for convinience:
A rigid rod of length $2a$ is suspended by two light, inextensible strings of length $l$ joining its ends to supports also a distance $2a$ apart and level ...
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1
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102
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Perturbation of central field potential
i`d like to consider system with Coulomb potential: $U = -\frac{\alpha}{r}$ and constant magnetic field.It is easy to write Lagrangian function:
$$ L = \frac{m}{2}(\dot{\rho}^2 + \rho^2\dot{\phi}^2) + ...
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Question about functional derivative computation in Quantum Field Theory for the Gifted Amateur
I'm confused about the evaluation of the functional derivative of Equation 1.12, $$J[f] = \int [f(y)]^p \phi(y) dy$$ on page 13 of Quantum Field Theory for the Gifted Amateur in Chapter 1.
Here are ...
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Four-divergence term in Lagrangian
It is known that adding a four-divergence term, $\partial_\mu A^\mu$ does not affect the equations of motion. I am trying to reason this based on the Euler-Lagrange equation. But I want to show this ...
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