Lagrangian Definition and 1000 Threads

Homework Statement Use the E-L equation to calculate the period of oscillation of a simple pendulum of length l and bob mass m in the small angle approximation. Assume now that the pendulum support is accelerated in the vertical direction at a rate a, find the period of oscillation. For what...

I've been watching Sidney Coleman's QFT lectures (http://www.physics.harvard.edu/about/Phys253.html, with notes at http://arxiv.org/pdf/1110.5013.pdf), and I'm now on to the spin 1/2 part of the course. We've gone through all the mechanics of constructing irreducible representations D^{(s1,s2)}...

I attached a file that shows the free EM action integral and how it can be rewritten. I would like to know how to go from the first line to the second. I have to integrate by parts somehow, and I know surface terms get thrown out, but I do not know how the indices of the gauge fields should be...

I've heard it said that the Lagrangian of a free particle cannot possibly be a function of any position coordinate, or individual velocity component, but it is a function of the total magnitude of velocity. Why is this the case? I'd be grateful for any pointers in the direction of either a...

Homework Statement Essentially the problem that I am trying to solve is the same as in this topic except that it is for 3 springs and 3 masses https://www.physicsforums.com/showthread.php?t=299905 Homework Equations I have found similar equations as in the topic but I face a problem in...

Homework Statement a) the lagrangian for a system of one degree of freedom can be written as. L= (m/2) (dq/dt)2sin2(wt) +q(dq/dt)sin(2wt) +(qw)2 what is the hamiltonian? is it conserved? b) introduce a new coordinate defined by Q = qsin(wt) find the lagrangian and hamiltonian...

Homework Statement A hollow semi-cylinder of negligible thickness, radius a and mass M can rotate without slipping over the horizontal plane z=0, with its axis parallel to the x-axis. On its inside a particle of mass m slides without friction, constrained to move in the y-z plane. This...

Hi all! Long story short, my QFT class recently covered gauge equivalence in QED, and this discussion got me thinking about more general gauge theory. I spent last weak reading about nonabelian symmetries (in the context of electroweak theory), and I like to think I now have a grasp on the...

Homework Statement I apologize if this is not the right place to put this. If it is not please redirect me for future reference. 11. Consider a uniform thin disk that rolls without slipping on a horizontal plane. A horizontal force is applied to the center of the disk and in a direction...

Homework Statement This isn't strictly a homework question as I've already graduated and now work as a web developer. However, I'm attempting to recover my ability to do physics (it's been a few months now) by working my way through the problems in Analytical Mechanics (Hand and Finch) in my...

Homework Statement A bead of mass m slides on a long straight wire which makes an angle alpha with, and rotates with constant angular velocity omega about, the upward vertical. Gravity acts vertically downard. a)Choose an appropriate generalized coordinate and find the Lagrangian. b)Write...

In Landau and Lifgarbagez, Vol. 1, it says "the component of angular momentum along any axis (say the z-axis) can be found by differentiation of the Lagrangian: M_{z} = \Sigma_{a} \partial L/\partial \dot{\varphi_{a}} where \varphi is the angle of rotation about the z axis. This is evident...

Homework Statement Greetings! This is an example problem at the end of Chapter 1 in Mechanics (Landau): A simple pendulum of mass m whose point of support oscillates horizontally in the plane of motion of the pendulum according to the law x=acos(\gamma t) . Find the Lagrangian...

Homework Statement A mass m is attached to one end of a light rod of length l. The other end of the rod is pivoted so that the rod can swing in a plane. The pivot rotates in the same plane at angular velocity \omega in a circle of radius R. Show that this "pendulum" behaves like a simple...

In QFT, Lagrangian is often mentioned. While in QM, it's the Hamiltonian, Is the direct answer because in QFT "position" of particle is focused on and Lagrangian is mostly about position and coordinate while in QM, potential is mostly focus on and Hamiltonian is mostly about potential and...

Hey, in general relativity, essentially I am asking how any metric (I.e. schwarzschild metric) was found. are the metrics derived or are they extrapolated from the correct lagrange equations of motion? If there is a derivation available, please provide a link. thanks

http://en.wikipedia.org/wiki/Lagrangian#Explanation I am trying to prove pV=nRT and in order to do so one need to get lagrangian (not the math formula it seems) Here is an explanation http://en.wikipedia.org/wiki/Lagrangian#Explanation why is \frac{\delta S}{\delta \varphi _i}=0...

I was wondering why when we derive the euler lagrange equations and when we use them we treat x and x dot as independent quantities?

So my text (Ryder 2nd edition, page 252) is defining the "pure gauge-field Lagrangian" as: G_{\mu \nu}\equiv \partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu}-ig\left[ A_{\mu},A_{\nu}\right] \mathcal{L} = -\frac{1}{4}Tr G_{\mu \nu} G^{\mu \nu} Dumb question: Isn't G_{\mu \nu} G^{\mu...

Homework Statement Hello. I have a problem with setting up the lagrangian for a system here. The problem is stated at page 8 problem 2.3 with a diagram at the following -->link<--- 2. The attempt at a solution I used two generalized coordinates corresponding to the angle between...

Does anybody know what interpretation the invariant corresponding to the global U(1) invariance of the Dirac Lagrangian is? I have always had it in my head that it's charge, but then I realized that uncharged free particles such as neutrinos satisfy this equation too! Any thoughts much...

Say we have a Lagrangian \mathcal{L}=\bar{u}i\kern+0.15em /\kern-0.65em Du+\bar{d}i\kern+0.15em /\kern-0.65em Dd-m_u\bar{u}u-m_d\bar{d}d, where u and d are fermions. In Peskin&Schroeder p. 667 it says that if m_u and m_d are very small, we can neglect the last two terms of the Lagrangian. I'd...

I have been calculating the currents and associated Noether charges for Lorentz transformations of the Dirac Lagrangian. Up to some spacetime signature dependent overall signs I get for the currents expressions in agreement with Eq. (5.74) in http://staff.science.uva.nl/~jsmit/qft07.pdf . What...

Hi, I have a following question... Can it be that there is given some Lagrangian and instead of considering whole Lagrangian one makes its series expansion and considers only some orders of expansion? Can you bring some examples or why and when does this happen... ? Thank you

Homework Statement Here's the free body diagram with variables. I am looking for the lagrangian mechanics equation. M is mass of the bottom wheel. m is the mass of the top wheel. R is the radius of the bottom wheel. r is the radius of the top wheel. θ_{1} is the angle from vertical of...

Hi, If I have three light quark flavours with massses m_u, m_d,m_s , I want to try and calcuate the masses of the eight pseudogoldstone bosons. I have found from my mass term in the Chiral L that: L_{mass}=-2v^3...

Homework Statement The goal of the question I'm being asked is to show that the covariant derivatives, D_{\mu}, "integrate by parts" in the same manner that the ordinary partial derivatives, \partial_{\mu} do. More precisely, the covariant derivatives act on the complex scalar field...

Homework Statement I have a problem regarding to lagrangian. If L is a Lagrangian for a system of n degrees of freedom satisfying Lagrange's equations, show by direct substitution that L' = L + \frac{d F(q_1,...,q_n,t)}{d t} also satisfies Lagrange's equations where F is any ARBITRARY BUT...

Hi! In some texts (Sakurai - advanced qm and others) I found this expression for the lagrangian of an em field: L=F_{\mu \nu}F_{\mu \nu} but I'm a bit confused... L must be a Lorentz invariant, so I would write instead: L=F_{\mu \nu}F^{\mu \nu} \;\; Which form is the correct one? Or...

Homework Statement I teach myself classical mechanics from David Tong http://www.damtp.cam.ac.uk/user/tong/dynamics.html From the homework set I should verify that the Lagrangian L=\frac{1}{12}m^{2}\dot{x}^{4}+m\dot{x}^{2}V-V^{2} Yields the same equations as the mere...

The Wikipedia article regarding Lagrangian Mechanics mentions that we can essentially derive a new set of equations of motion, thought albeit non-linear ODEs, using Lagrangian Mechanics. My question is: how difficult is it usually to solve these non-linear ODEs? What are the usual numerical...

Hi, If I have the Lagrangian L=i\chi^{\dagger\alpha i}\bar{\sigma}^{\mu}(D_{\mu})_{\alpha}^{\beta}\chi_{\beta i}+i\xi^{\dagger}_{\bar{i}\alpha}\bar{\sigma}^{\mu}(\bar{D}_{\mu})^{\alpha}_{\beta}\xi^{\beta i}-1/4 F^{a\mu\nu}F_{\mu\nu}^{a} where \alpha,\beta are colour indices, and i=1,2 is a...

Please teach me this: Why the Lagrangian in QFT must involve derivative of field? Is it correct that because fermions and bosons(meaning all things) obey Dirac and Klein-Gordon equations,then the corresponding Lagrangians include the derivative of field? (I know that the derivative has a...

Homework Statement A particle of mass m is placed on the inside of a smooth paraboloid of revolution whose equation is cz = x2 + y2 , where c is a constant, at a point P which is at a height H above the horizontal x-y plane. Assuming that the particle starts from rest (a) find the speed...

The stress-energy tensor is usually defined in standard GR treatments as T_{\mu\nu} = -\frac{2}{\sqrt{-g}}\frac{\delta(\sqrt{g}L_m)}{\delta g^{\mu\nu}}) with the Lm the matter Lagrangian. I'm curious what Lm is for a perfect fluid with density ρ and pressure P that would lead to the...

Homework Statement a.) Set up the Lagrange Equations of motion in spherical coordinates, ρ,θ, \phi for a particle of mass m subject to a force whose spherical components are F_{\rho},F_{\theta},F_{\phi}. This is just the first part of the problem but the other parts do not seem so bad...

Please teach me this: Does a symmetry of Lagrangian be reserved in each Feynman diagram of perturbative QFT,because even Ward Identity still deduces from U(1) symmetry that we consider each diagram has?. By the way, does effective action reserve the symmetry that Lagrangian has?. Thank...

Hi guys, can you help me with this? I'm supposed to calculate the energy momentum for the classic Maxwell Lagrangian, \mathcal{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu} , where F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu with the well known formula: T^{\sigma\rho}=\frac{\delta\mathcal{L}}{\delta...

Homework Statement |--------------------| m|----------m-------- |m |--------------------| -------> x : positive x-axis This is a picture of a coupled oscillator in equilibrium. All three masses are equal and the spring constant on the long springs are k and the two short...

Homework Statement Q) A child, Alice, on a playground merry-go-round can be modeled as a point mass m on a homogeneous horizontal disc of mass M and radius a. The disc rotates without friction about a vertical axis through its center. Alice clings to a straight railing that extends from the...

Homework Statement "A bead with mass m slides without friction on a wire which lies in a vertical plane near the earth. The wire lies in the x-z plane and is bent into a shape conforming to the parabola az = x2, where a is a positive known constant. (X is horizontal and z is vertical) The...

Please teach me this: Why the Lagrangian in QFT does not include high order derivative of field?Is it correct the reason being all fields obey the only Dirac and Klein-Gordon equations? Thank you very much for your kind helping.

Is anyone good with Lagrangian mechanics applied to constrained systems? I had a question about the Lagrange multiplier method, maybe I should have posted it in this section. https://www.physicsforums.com/showthread.php?t=550139

I know that it works with adding a total time derivative and multiplying the Lagrangian by a constant. are these the only things that can be done to a Lagrangian such that the equations of motion have the same solutions q(t). Thanks!

Man I hate to make two post in one day but I am really stuck! Homework Statement A particle slides on the inside surface if a frictionless cone. The cone is fixed with its tip on the ground and its axis vertical. The half angle of the tip is α. Let r be the distance from the particle to the...

Homework Statement Two equal masses are glued to a massless hoop of radius R that is free to rotate about its center in a vertical plane. The angle between the masses is 2*theta. Find the frequency of small oscillations.Homework Equations \frac{d}{dt} \frac{∂L}{∂\dot{q}}=\frac{∂L}{∂q} The...

In Landau's Mechanics, if an inertial frame \textit{K} is moving with an infinitesimal velocity \textbf{ε} relative to another inertial frame \textit{K'}, then \textbf{v}'=\textbf{v}+\textbf{ε}. Since the equations of motion must have the same form in every frame, the Lagrangian L(v^2) must be...

Hi everyone Homework Statement At first I want to find the langrangian function and the equation of motion for a system which exists of 2 masses(m) coupled by a spring(k). It's moving in 3 dimensions.We shall use cylindrical coordinatesHomework Equations LangrangianThe Attempt at a Solution...

I am trying to find the equations of motion for a test particle in the schwarzschild metric. However, I cannot find the correct first integral for the Lagrangian. The Schwarzschild metric is: ds^2 =...

Homework Statement Find the Lagrangian of a simple pendulum of mass m whose point of support moves uniformly on a vertical circle with constant angular velocity. (So basically there is a circle around the origin that spins with a constant angular velocity and the pendulum is attached to the...