Lagrangian Definition and 1000 Threads

Homework Statement A cart of mass M is attached to a spring with spring constant k. Also, a T-shaped pendulum is pinned to its center. The pendulum is made up of two bars with length L and mass m. Find Lagrange's equations of motion. I've attached the figure and my solution as a PDF. I...

Homework Statement A point mass m slides without friction on a horizontal table at one end of a massless spring of natural length a and spring constant k. The other end of the spring is attached to the table so that it can rotate freely without friction. The spring is driven by a motor...

I'm thinking about generalizations of Lagrangian mechanics to systems with infinitely many degrees of freedom, but what I've got uses some extremely sketchy math that still appears to give a correct result. I only consider conservative systems that do not explicitly depend on time. Of course...

Hi I'm trying to define a Newtonian lagrangian in an rotating reference frame (with no potential) Something to note is that the time derivative of in a rotating reference frame must be corrected for by: \frac{d {\bf B}}{dt} \rightarrow \frac{d {\bf B}}{dt} + {\bf \omega} \times {\bf...

Homework Statement Consider the Lagrangian of a particle moving in a potential field L = m/2( \dot{x}2 + \dot{y}2 + \dot{z}2) - U(r), r = sqrt(x^2 + y^2) (a) Introduce the cylindrical coordinates and derive an expression for the Lagrangian in terms of the coordinates. (b) Identify the...

how we can explain the differential of lagrangian is a perfect ?L dt

if the lagrangian is time homogenous ,the hamiltonian is a constant of the motion . Is this statement correct ?

What is meant by Lagrangian of a dynamical system? Explain the same for N particle system.

Homework Statement I'm confused. Some websites say it is dL/dx = d/dt dL/dv, whereas others say it is the equations of acceleration, velocity and displacement derived from this, which would require integration, yes? Homework Equations The Attempt at a Solution

Homework Statement Consider a vertical plane in a constant gravitational field. Let the origin of a coordinate system be located at some point in this plane. A particle of mass m moves in the vertical plane under the influence of gravity and under the influence of an aditional force f =...

Homework Statement There is a joint system of rods and masses.We need to set up Lagrangian. Homework Equations L= T-V , T = Kinetic energy , V = Potential energy The Attempt at a Solution Hey what should we take as the zero of potential. So does the Lagrangian depend on the zero...

Hi, I'm trying to use calculus of variations to solve for the probability distribution with highest entropy for a given covariance matrix. I want to maximize this: H[p(\vec{x})] = -\int p(\vec{x})*ln(p(\vec{x}))d\vec{x} with the following constraints: \int p(\vec{x}) = 1 \int...

Is there a derivation for the classical electrodynamic Lagrangian? I have taken a look at a few textbooks that I have on hand but all of them just state the Lagrangian (in the voodoo four-vector talk, \glares) without explaining the reasoning behind it. I know that the Lagrangian for a charged...

Hi all, As a blind follower of QFT from the sidelines (the joys of the woefully inadequate teaching of theory to exp. particle physics students...), I have just realized that I've never actually gone further than deriving the Dirac equation, and then just used the Dirac Lagrangian density as...

The Lagrangian \mathcal L =\psi^{\dagger}\gamma^0 \gamma^\mu (1-\gamma^5)\partial_\mu \psi should violate parity, but I'm getting that it doesn't. \psi(x) changes to \gamma^0 \psi( Px) where Px=(t,-x) and x=(t,x). \gamma^j goes to - \gamma^j , while \gamma^0 stays the same...

Homework Statement A system consists of 3 identical masses (A,B & C) in a line, connected by 2 springs of spring constant k. Motion is restricted to 1 dimension. at t=0 the masses are at rest. Mass A is the subjected to a driving force given by: F=F0*cos(omega*t) Calculate the...

My background is electrical engineering, but I've recently become fascinated with the principle of least action. I've gone to library to look at a few books on the subject, but I've quickly become overwhelmed. Is there a good book/video lectures on Lagrangian Mechanics for somebody who...

Homework Statement Spring-mass system on a frictionless surface. A pendulum hangs from the mass of the spring-mass system. Write the Lagrangian.The Attempt at a Solution Take x as the stretch from equilibrium of the spring and k its elastic constant. M is the mass on the spring. Take \theta...

According to Landau textbook: Having two inertial frames K and K' moving with velocities \vec{v} and \vec{v'}=\vec{v} + \vec{\epsilon} where \vec{\epsilon} is an infinitesimal. We have L' = L(v'^2) = L (v^2 + 2 \vec{v} \cdot \vec{\epsilon} + \epsilon^2). Expanding this expression in powers of...

does anyone have any suggestions for websites (and or books) that have some decently simple solved Lagrangian problems that i could try to solve as practice. I'm just a beginner so the simpler it is the better. Also any websites or books that might be good for explanations of Lagrangians.

What is the general rule behind why for any given lagrangian (QED/QCD show this) that any vectors or tensors contract indices? I know it must be something simple, but I just can't think of it offhand. QED : F_{\mu\nu}F^{\mu\nu} Proca (massive vector): A_\mu A^\mu QCD : G^{\alpha}_{\mu\nu}...

Does anyone have a high resolution picture of the standard model lagrangian? i want to put it on a t shirt and give it to my math teacher who worked at Bell Laboratories for 10 years and knows just about everything about physics and math. P.S. i only think its called the standard model...

Hello, I read somewhere that the second derivatives of coordinates in Lagrangian would violate causality. Why is this so? Does that mean that the whole concept of jerky mechanics violates causality? Thanks

Does anyone know of a treatment of Lagrangian and/or Hamiltonian mechanics that would be accessible to someone who is (or was, about forty years ago) reasonably fluent in elementary calculus and Newtonian mechanics? I am less interested in a college textbook than in an overview a la Brian...

Is there a simple way to understand why the Lagrangian of the classical electrodynamic field is (in SI units) E^2/2 e0 - B^2/2 mu0 ? Why is there a minus in it? Is there some simple, intuitive explanation for it? Heinz

I'm not sure if this is in the right section, if it isn't can someone please move it :) Lagrangian mechanics has me completely stumped. Just doesn't seem to make any sense to me. So let's see how this goes. A best of mass m is threaded onto a frictionless wire and allowed to move under the...

Homework Statement Consider the Proca Lagrangian L=-\frac{1}{16\pi}F^2-\frac{1}{c}J_{\mu}A^{\mu}+\frac{M^2}{8\pi}A_{\mu}A^{\mu} in the Lorentz gauge \partial_{\mu}A^{\mu}=0 Find the equation of motion. Homework Equations F^2=F_{\mu\nu}F^{\mu\nu} The Attempt at a...

I've just encountered the terms Hamiltonian and Lagrangian. I've read that the Hamiltonian is the total energy H = T + U, while the Lagrangian L = T - U, where T is kinetic energy, and U potential energy. In the case of Newtonian gravitational potential energy, U = -G\frac{Mm}{r}. So am I...

Hi, May anybody tell the pre-reqs (on calculus) for learn the lagrangian formalism used on quantum field theory ? :confused: Thanks.

HELP! I am currently working on the derivation of the equations of motion for three coupled pendula, The mass and length of each pendulum is the same, but the central pendulum has some sort of resistive degenerative force due to submersion in a liquid. I have calculated the normal modes...

We know the covariant Lagrangian of the Lorentz force law. However, in presence of a magnetic monopole, one must add another term to the force law. This term, of course is the Dual Field Tensor, along with the magnetic charge 'g' as follows - m \frac{d^2 x^{\mu}}{d {\tau}^2} =...

I believe there is a way of calculating Christoffel symbols which is easier and less time-consuming than using the metric formula directly. This involves writing down the Lagrangian in a form that just includes the kinetic energy assuming zero potential energy and then equating the coefficient...

Investigating how a car bounces with the framework of an idealized model. Let the chassis be a rigid, square plate, of side a and mass M, whose corners are supported by massless springs, with spring constants K,K,K and k < K (the faulty one). The springs are confined so they stretch and compress...

Homework Statement ______|equillibrium position________ ______|__i_____________________ m^^^^^m^^^^^m^^^^^m^^^^^m ____k_|qi|____k______ k________kA collection of particles each of mass m separated by springs with spring constant k. The displacement of the ith mass from its equilibrium position...

Homework Statement I'm trying to derive the Klein-Gordon equation from its lagrangian density \mathcal{L} = - \frac{1}{2} \partial^{\mu} \varphi \partial_{\mu} \varphi - \frac{1}{2} m^2 \varphi^2 + \Omega_0 (Srednicki p.24) Homework Equations S = \int d^4x \mathcal{L}...

Homework Statement A spring of negligible mass and spring constant k, hanging vertically with one end at a fixed point O, supports a mass m, and beneath it as second, identical spring carrying a second, identical mass. Using a generalised coordinates the vertical displacements x and y of...

1). A bead is confined to moving on a wire in the shape of a porabola, given by y=bx^2. Write down the Lagrangian, with x as the generalized coordinate, and the equations of motion for this sytem. We have L(x, bx^2) For writing out the Lagrangian as a function of x, I get.: L = m/2((xdot)...

How does lagrange multipliers work? i was able to work out this proof of the idea, but its only true for a function with two independent variables and one dependent variable. Rn=the space that is the independent variables. x[Rn]=x C[Rn]=C=constant. dx/d[Rn]=grad(x)*v; v is a unit...

Homework Statement A uniform circular pulley of mass 2m can rotate freely about its axis of symmetry which is fixed in a horizontal position. Two masses m, 3m are connected by a massless string which passes over the pulley without slipping. The whole system undergoes planar motion with the...

while studying lagrangian i got this doubt..if the lagrangian is invariant in time,space,rotation, then we have corresponding conservation laws.. In spontaneous symmetry breaking, the lagrangian is not invariant in ground state and the symmetry breaks spontaneously.so, the conserved quantity is...

Hello everyone, I'm not sure if these questions are really trivial or of they're a little subtle... but here goes. 1. In Ramond's text (Field Theory: A Modern Primer), he explains that the Lagrangian for fermions should have the derivative operator antisymmetrized in order for the kinetic...

Homework Statement http://img261.imageshack.us/img261/5923/14254560bc0.th.jpg the question is in the image exactly as i wrote it down in class. but it's basically asking what systems have potential and kinetic energies that form a Lagrangian which is invariant to some transformation...

Hi, I am trying to solve this problem here: http://img201.imageshack.us/img201/7006/springqo9.jpg We're supposed to find the equation of motion from the lagrangian and not Newton's equations. Attempted solution: L = T - U = \frac{I\omega^2}{2} + \frac{mv^2}{2} - \frac{kr^2}{2} I = m(r^2 +...

If you have a Lagrangian of the form: L=\phi \partial^2 \phi how would you derive its equation of motion? All the books seem to say to treat this Lagrangian as if it were only a function of the field, and not derivatives of the field. So to calculate this they seem to do a product rule...

Another Lagrangian problem: Bead sliding along a horizontal rotating ring Homework Statement A horizontal ring of mass M and radius a rotates freely about a vertical axis passing through a point on its circumference. If a bead of mass m slides along the ring without friction, what is the...

Homework Statement Imagine a spatially 2d world. The electromagnetic field could be richer here, because you could add to the Lagrangian L an additional term (known as the Chern-Simons Lagrangian) L_{CS} = \epsilon_{0}\frac{\kappa}{2}\epsilon^{\alpha \beta...

Homework Statement Determine the kinetic energy of a bead of mass m which slides along a frictionless wire bent in the shape of a parabola of equation y = x2. The wire rotates at a constant angular velocity \omega about the y-axis. Homework Equations T = \frac{1}{2}m(\dot{x}^2 +...

In http://en.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism It is written: \mathcal{L} \, = \, \mathcal{L}_{\mathrm{field}} + \mathcal{L}_{\mathrm{int}} = - \frac{1}{4 \mu_0} F^{\alpha \beta} F_{\alpha \beta} + A_{\alpha} J^{\alpha} \,. a personal...

A Lagrangian approach to the Barrett-Crane spin foam model--Livine Bonzom Here's a paper helping to sort out the situation with spinfoams. I think it is probably important. Actually we've been anticipating something of this caliber. Back in October I put in a placeholder for an expected Livine...

Homework Statement Write down the Lagrangian for a cylinder mass m, radius R an moment of inertia I, that rolls without slipping straight down an inclined plane which is at an angle a from the horizontal. Use as your generalized coordinate the cylinder's distance x measure down the plane...