# Tagged Questions

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### Use of the term first order dependency

In a question I am doing it says: Show explicitly that the function $$y(t)=\frac{-gt^2}{2}+\epsilon t(t-1)$$ yields an action that has no first order dependency on $\epsilon$. Also my textbook ...
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### The variation of the Lagrangian density under an infinitesimal Lorentz transformation

I'm trying to introduce myself to QFT following these lectures by David Tong. I've started with lecture 1 (Classical Field Theory) and I'm trying to prove that under an infinitesimal Lorentz ...
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### Hoop rolling inside a circular hole

A hoop of radius $b$ and mass $m$ rolls without slipping within a stationary circular hole of radius $a > b$ and is subject to gravity. Use the generalized coordinates the rotation angle $\phi$ of ...
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### Finding the magnetic vector potential by calculus of variations

Given the functional $$F[A]=\int_{\mathbb{R}^3}\{\frac{1}{2\mu(x)}|\nabla\times\vec{A}|^2-\vec{J}\cdot\vec{A}\}d^3x$$ with $\vec{A}$ is a candidate vector potential for the field ...
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### Restrained double pendulum

The equations of motion of a double pendulum are well-known. Usually you'd have the them expressed in the rotations $\theta_1(t)$ and $\theta_2(t)$. There are two degrees of freedom. Now consider the ...
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### Potential energy of an infinitesimal length of elastic rod

I am having an embarrassingly hard time with the derivation for the potential energy of an infinitesimal element of an elastic rod of area A. The picture shown below is an element of the rod that has ...
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### Lagrangian for a moving spring device [closed]

How can I write the proper Lagrangian for such as system as the one shown in picture? Am confused about what is the suitable way to designate the coordinate.
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### Lagrangian approach to spinning thread reel

I am trying to better understand Lagrangian dynamics and am struggling to complete the following question: A reel of thread of mass $m$ and radius $r$ is allowed to unwind under gravity, the upper ...
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### $\cos^{2}(\phi)$ in the kinetic energy term of the Lagrangian is one?

I'm doing some homework in Classical Mechanics, and is about to write out the Lagrangian of a system. But, when I check the answer from my teacher, something is missing. The kinetic energy I'm using ...
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### From Lagrangian to equations of motion [closed]

I have a given Lagrangian: $$L= e^{st}\cdot\frac12\cdot(mv_y^2-ky^2)$$ And are asked to identify the equations of motions, the constants of motions and physical system. Without the exp-time-term, ...
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### Pendulum with a rotating point of support from Landau-Lifschitz

I found this problem in Landau-Lifschitz vol.1 (Mechanics) A simple pendulum of mass $m$, length $l$ whose point of support moves uniformly on a vertical circle with constant frequency $\gamma$. ...
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### How do I obtain the Lagrangian in standard for using action? [closed]

I have action as shown below $$S=\int \mathrm{d}t \int \mathrm{d}x^3 \bar\psi\left(i\partial_t\psi +\frac1{2m}\bar\nabla^2\psi-V(x)\psi\right)$$ How do I manipulate it to obtain the Lagrangian ...
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I have to find the Lagrangian for a system. In the point of interest I have come up with the following position coordinates: $$x = Rcos(\omega t)+\ell sin(\phi)$$ and $$y = Rsin(\omega t)-\ell ... 1answer 92 views ### Nonlinear Klein Gordon equation For the Klein Gordon nonlinear equation,$$ u_{tt}- \Delta u +f(u)=0,$$how could I use Noether's theorem to prove that there is a conserved quantity? I.e.,$$ (\Pi _{k} )_{t} - \rm div(j_{k})=0 $$... 0answers 108 views ### Finding moment of inertia from Lagrange equation I'm getting the following information: Consider a system consisting of two rotating bars of length \ell and with uniform mass density and each with total mass m. The bars are attached to a common ... 1answer 217 views ### Optimal selection of generalized coordinates in Lagrangian system EDITED: The number of bonds is actually 2, not 1 (look at edit history). Fixed for archiving purposes. Problem: The edge A of an homogeneous rod (of length \ell and mass m) is performing a smooth ... 1answer 91 views ### How to find the equillibrium points using Jacobian and Hessian? Given that I have Jacobian and Hessian matrices of three particles interacting with each other in a harmonic trap through Coulomb's law in a 2D plane, how do I find the equilibrium points of them (I ... 1answer 109 views ### Block on cart, equation of motion Consider a rigid block of b \times h having mass m on cart (as depicted below). The cart is given an acceleration a, this leads to overturning of the block. The angle of rotation is indicated by ... 0answers 66 views ### Spring Force in a Dynamic Equation I am working on dynamic simulation of a bipedal robot, I have dynamic equations of a preliminary structure. But Now I have to add some springs to the dynamics. I am having a problem of how to account ... 1answer 236 views ### Is there a better choice of coordinates for a bead on a rotating helical wire? A bead of mass m is threaded around a smooth spiral wire and slides downwards without friction due to gravity. The z-axis points upwards vertically. Suppose the spiral wire is rotated about the ... 0answers 404 views ### Ball rolling without slipping inside a hollow cylinder A small ball of radius r performes small oscillations within a hollow cylinder of radius R. What would be the angular frequency of the oscillations given that the rolling is without slipping? The ... 0answers 26 views ### Expansion of L(v^2 + 2\vec{v}\cdot\vec{\epsilon}+\epsilon^2) [duplicate] How can I find the expansion of the Lagragian (it it only dependent on v^2) L(v^2 + 2\vec{v}\cdot\vec{\epsilon}+\epsilon^2) in powers of \vec{\epsilon} ? (From L.Landau, E. Lifshitz, Mechanics , ... 1answer 163 views ### Lorentz force equation from relativistic Lagrangian The relativistic Lagrangian is given by$$L = - m_0 c^2 \sqrt{1 - \frac{u^2}{c^2}} + \frac{q}{c} (\vec u \cdot \vec A) - q \Phi $$I need to derive, \displaystyle \frac{d\vec p}{dt} = q \left( \vec E ... 1answer 184 views ### Calculate Hamiltonian from Lagrangian for electromagnetic field I am unable to derive the Hamiltonian for the electromagnetic field, starting out with the Lagrangian$$ \mathcal{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}-\frac{1}{2}\partial_\nu A^\nu \partial_\mu A^\mu ...
Nordstrom's theory of a particle moving in the presence of a scalar field $\varphi (x)$ is given by  S = -m\int e^{\varphi (x)}\sqrt{\eta_{\alpha \beta}\frac{dx^{\alpha}}{d ...