Lagrangian Definition and 1000 Threads

Another Exercise... Ohanian Exercise 6 The Euler-Lagrange Equation given: ##\frac{\partial}{\partial x^\mu} \frac{\partial \mathcal{L}}{\partial (\partial_\mu h^{\alpha\beta})} - \frac{\partial \mathcal{L}}{\partial h^{\alpha\beta}} = 0## ##\frac{\partial \mathcal{L}}{\partial...

I was working on an exercise in Ohanian's book. [Appendix A3, page 484, Exercise 5] I guess he means charge conservation, but wrote ##j^\nu = 0##. The Lagrangian was given by ##\mathcal{L}_{em} = -\frac{1}{16\pi} \left( A_{\mu ,\nu} - A_{\nu ,\mu} \right) \left( A^{\mu ,\nu} - A^{\nu...

I am watching Susskind's derivation of Newton's F=ma from the Euler-Lagrange equations (53 minutes in) here for which he uses the Lagrangian of kinetic energy minus potential energy. I have seen this done elsewhere as well. As far as I can tell, and please correct me if I'm wrong, the only...

I've been reading a lot about path integrals lately, and I've found it fascinating to see at the quantum level how the extremal values of the lagrangian are basically the only ones that contribute when the action is large and therefore we get the classical path. Something that continues to...

Hello, I have the functional J = ∫ L(ψ, r, r') dψ, where r'=dr/dψ. L is written in polar coordinates (r,ψ). Now I want to constrain the motion to take place on the polar curve r = r(ψ). Can I write the constrained lagrangian as Lc=L(ψ, r, r') - λ(r - r(ψ)) and then solve the...

Homework Statement (context: I'm studying for a test, and this is a question from a past exam paper.) "A wedge of mass M with angle \phi is free to slide on a frictionless horizontal table. A solid ball of radius a and mass m is placed on the slope of the wedge. The contact between the ball...

Hi! I tried to compute an ideal barbell-shaped object's dynamics, but my results were wrong. My Langrangian is: ## L = \frac{m}{2} ( \dot{x_1}^2 + \dot{x_2}^2 + \dot{y_1}^2 + \dot{y_2}^2 ) - U( x_1 , y_1 ) - U ( x_2 , y_2 ) ## And the constraint is: ## f = ( x_1 - x_2 )^2 + ( y_1 -...

I'm trying to figure out when is \frac{\delta L}{\delta p}=\dot{q} . From L=p\frac{\delta H}{\delta p}-H I get that \frac{\delta L}{\delta p}=p\frac{\delta^2 H}{\delta p^2}=p \frac{d}{dp}\dot{q} . For this to equal just \dot{q} , it must obey the dfe \frac{d}{d ln p}\dot{q}=\dot{q}...

Let say I want to study electron-proton scattering (without considering proton's quarks, i.e. no QCD), which is the Lagrangian? I've seen two different answers to this question :confused: First one: L=\bar{ψ}e(i∂-me)ψe+\bar{ψ}p(i∂-mp)ψp-\frac{1}{4}Fμ\nuFμ\nu-e\bar{ψ}eγμψeAμ+e\bar{ψ}pγμψpAμ...

Is the lagrangian used in QFt because its the only information of motion we can obtain about a system at relativistic speeds? Does the lagrangian reflect the conservation of energy ? Is this why the lagrangian must be invariant... Meaning that it must be constant... Meaning that energy is...

Homework Statement Thank you for answering my question about setting the Euler-Langrangian expression to zero separately for each coordinate (ehild ans.=yes). Now my question is: Can the Lagrangian be derived, or is it the expression, when inserted into the Euler-Lagrange equation(s), that...

Homework Statement Consider the setup shown in the gure below. The cart of mass M moves along the (horizontal) x axis. A second mass m is suspended at the end of a rigid, massless rod of length L. The rod is attached to the cart at point A, and is free to pivot about A in the x-y plane...

So I was going through an ODEs textbook and in a section discussing physical problems, decided that it would be interesting to come up with the equations of motion using Lagrangian mechanics for the examples they posted. For the first example, a falling rock, this easily worked. The second...

No this is not homework. http://imgur.com/zAZxmuC http://imgur.com/zAZxmuC Ok i am struggling to even start this question. I see it has a constraint so i would be tempted to use Lagrangian but from there i don't see how px and qy fit into it? Some assistance on the tools needed to...

Homework Statement Write down the Lagrangian for a one-dimensional particle moving along the x-axis and subject to a force: F=-kx (with k positive). Find the Lagrange equation of motion and solve it. Homework Equations Lagrange: L=T-U (kinetic energy - potential energy) The Attempt...

In reading Ryder's book on quantum field theory he advocates reading off the Feynman rules directly from the Lagrangian in the path integral quantization method. I can sort of do this in phi-four theory, but it is not obvious in for example Yang-Mills theory, so I wondered if someone could...

Hey, I'm having trouble with part (d) of the question displayed below: I reckon I'm doing the θ Euler-Lagrange equation wrong, I get : \frac{\mathrm{d} }{\mathrm{d} t}(\frac{\partial L}{\partial \dot{\theta}})-\frac{\partial L}{\partial \theta}=\frac{\mathrm{d} }{\mathrm{d}...

Hi we covered the Lagrange multiplier method in Lagrangian Mechanics and as far as I know, is the physical meaning behind this to be able to solve either some non-holonomic constraints or to get some information about the constraint forces. my problem is, i do not know the physical meaning of...

I'm trying to derive the Geodesic equation, \ddot{x}^{α} + {Γ}^{α}_{βγ} \dot{x}^{β} \dot{x}^{γ} = 0. However, when I take the Lagrangian to be {L} = {g}_{γβ} \dot{x}^{γ} \dot{x}^{β}, and I'm taking \frac{\partial {L}}{\partial \dot{x}^{α}}, I don't understand why the partial derivative of...

Hi guys, So textbooks have it that: "Two Lagrangians differing by a total time-derivative of a function of the coordinates are equivalent". I have no idea what that means or how to use it; so I don't know which terms I can drop from Lagrangians, which is a bit of a problem. For example...

Homework Statement Consider a particle of mass m and electric charge e subject to a uniform electromagnetic field (E(x,t),B(x,t)). We must remember that the force they exert is given by: F = cE(x,t) + ex' \times B(x,t) A principle of action that represents such particle subject to the...

Homework Statement A mouse of mass m runs around the inner circumference of a vertical wheel which is free to rotate about the centre. The wheel has mass M and moment of inertia I. Let θ be the angle that the radius vector makes to the mouse from the downward vertical at time t. Write down the...

Homework Statement Consider the Atwood’s pulley shown below. The masses are 4m, 3m, and m. Let x and y be the directed distances from the centers of the fixed (i.e. inertial) top pulleys for the left and right masses as indicated. http://imgur.com/VXEygxt a) Write down the Lagrangian...

Hi, I hope I put this in the right place! I'm having trouble with some of the calculus in moving from the Klein-Gordin Lagrangian density to the equations of motion. The density is: L = \frac{1}{2}\left[ (\partial_μ\phi)(\partial^\mu \phi) - m^2\phi ^2 \right] Now, to apply the...

Hi there, I'm having some problems trying to write down the Lagrangian of the following system: A uniform flexible chain of mass M and length L is hung under gravity on a frictional pulley of radius a and moment of inertia I whose axle is fixed at a point above the ground. Write down the...

Let \gamma^{\rho} \in M_{4}(\mathbb{R}) be the Majorana representation of the Dirac algebra (in spacetime signature \eta_{00} = -1), and consider the Majorana Lagrangian \mathcal{L} = \mathrm{i} \theta^{\mathrm{T}} \gamma^{0} (\gamma^{\rho} \partial_{\rho} - m) \theta, where \theta is a...

I've been tasked with showing that a Lagrangian under a set of transformations changes by a time derivative. All has gone well, except I'm left with two remaining terms, that I am completely confident, aren't there by mistake (as the 16 terms that should be expected have all popped out with the...

Is: \mathcal L=-\frac{m}{2} u^\alpha u_\alpha a correct Lagrangian for SR (assuming the parameter is proper time rather than world time)? It leads to the correct EOM when plugged into the Euler-Lagrange equation, m\frac{du^\alpha}{ds}=0 Or is this the correct Lagrangian: \mathcal L=-m...

Homework Statement Consider the following Lagrangian: L = \frac{m}{2}(x'^2+y'^2+z'^2) + \frac{q}{2}(xy'-yx') Where q denotes a charged particle. a) Find the equations of motion b) Find the solution for z c) Find the solution in the x-y plane, and prove that it corresponds to an oscillatory...

what is Lagrangian ? the Hamiltonian H = T + V represents the total energy of the system, and Lagrangian L = T-V, but what does it actually represents and what is the exact meaning of Lagrangian ? it represents excess energy or energy loss or some thing else ?

Write down the Lagrangian $\mathcal{L}(x_1,x_2,\dot{x}_1,\dot{x}_2)$ for two particles of equal masses, $m_1 = m_2 = m$, confined to the $x$ axis and connected by a spring with potential energy $U = \frac{1}{2}kx^2$. [Here $x$ is the extension of the spring, $x = (x_1 - x_2 - \ell)$ where $\ell$...

Homework Statement Find Scl for a particle under constant force f, that is: L = (m/2)v2 + fx Homework Equations S = ∫Ldt d(∂L/∂q^{.})/dt = ∂L/∂q The Attempt at a Solution Apologies if this belongs in the Introductory Physics section. Apologies for terrible formatting...

Homework Statement Hi guys. http://img189.imageshack.us/img189/5123/systemn.jpg The image shows the situation. A pointlike particle of mass m is free to move without friction along a horizontal line. It is connected to a spring of constant k, which is connected to the origin O. A...

Homework Statement A particle of mass m moves on the surface of a paraboloidal bowl with position given by r=rcosθi+rsinθj+\frac{r^{2}}{a}k with a>0 constant. The particle is subject to a gravitational force F=-mgk but no other external forces. Show that a suitable Lagrangian for the system is...

Homework Statement So we have started Lagrangian Mechanics in my class, and I really don't understand it at all. My teacher keeps doing the math on the board, but he hasn't really said what a Lagrangian is, and what an Action is. I really am lost from the start with these problems. Any help...

In the attached snip, the last few steps of the lagrangian equation is shown. I don't understand how the \frac{\delta V}{\delta\dot{q_j}}= 0. As an example let me take gravitational force. With change in velocity ( along the downwards direction obviously), there sure is a change in gravitational...

I understand how to use Hamiltonian mechanics, but I never understood why you construct the Hamilitonian by first constructing the Langrangian, and then performing a Legendre transform on it. Why can't you just construct the Hamiltonian directly? Does it have to do with the generalized...

Homework Statement Show that the free particle lagrangian is invariant to rotations in $$\Re^{3}$$, but I assume this means invariant up to a gauge term. $$L=m/2 [\dot{R^{2}} + R^{2}\dot{θ^{2}} +R^{2}Sin^{2}(θ)\dot{\phi^{2}}$$ Homework Equations I consider an aribtrary infinitesimal...

Homework Statement Homework Equations The Attempt at a Solution I don't understand where the third term from the first equation of 5.192 come about.. as clearly L doesn't depend on x at all, so ∂L/∂x should be zero.

Homework Statement Find two independent conserved quantities for a system with Lagrangian L = A\dot{q}^{2}_{1} + B\dot{q_{1}}\dot{q_{2}} + C\dot{q}^{2}_{2} - D(2q_{1}-q_{2})^{4}\dot{q_{2}} where A, B, C, and D are constants. Homework Equations None.The Attempt at a Solution I've only found...

Hello.I recently discovered the Lagrangian approach on classical mechanics ptovlems, such as a spring pendullum, or even on particle physics problems, and i think it s a really smart way of getting results. I'd like to approach this method deeper and so my questions are the following: 1.What...

I've been doing some self-study in Peskin and Schroeder and been struggling a bit in Part III. Right now, I am stuck on the last two terms in 16.6 (Lagrangian for Yang-Mills). Presumably these come from (-1/4) (F^{a}_{\mu\nu})^2, but I am getting stuck on getting the indices to work out...

Homework Statement The Lagrange method does work for some velocity dependent Lagrangian. A very important case is a charged particle moving in a magnetic field. The magnetic field can be represented as a "curl" of a vector potential ∇B = ∇xA . A uniform magnetic field B0 corresponds to a vector...

I wanted to solve the problem of a cone rotating on its side over a table, around an axis that pass through it's apex, like in the figure. What I want to find is the angular speed ω, the spin of the solid, such that the cone "stands" over it's apex. I don't know how to set the condition...

There's a specific problem I'm doing, but this is more of a general question. The setup is a cylinder of mass m and radius R rolling without slipping down a wedge inclined at angle \alpha of mass M, where the wedge rests on a frictionless surface. I've made the Cartesian axis centred at the...

Here and there I come across the following formula for the Lagrangian density of a real scalar field, but not a deriviation. \mathcal{L} = \frac {1}{2} [ \dot \phi ^2 - ( \nabla \phi ) ^2 - (m \phi )^2 ] Could someone show me where this comes from? The m squared term in particular...

Homework Statement Carry out the integration ψ = ∫[M(dr/r2)] / √(2m(E-U(r)) - (M2/r2)) E = energy, U = potential, M = angular momentum using the substitution: u = 1/r for U = -α/r Homework Equations The Attempt at a Solution This is as far as I've gotten: -∫ (Mdu) /...

Homework Statement 2 masses, m_{1} and m_{2} are fixed at the endpoints of a rigid rod of length l. mass m_{1} is attached to a horizontal bar so that it may move in the x direction freely, but not in the y direction. let θ be the angle the rod makes with the vertical, what is the...

Homework Statement The problem asked us to show that the Euler-Lagrange's equations are invariant under a point transformation q_{i}=q_{i}(s_{1},...,s_{n},t), i=1...n. Give a physical interpretation. Homework Equations \frac{d}{dt}(\frac{\partial L}{\partial \dot{s_{j}}})=\frac{\partial...

Homework Statement We are given L = 1/2mv2 - mgz. a) Find the equations of motion. b) Take x(0) [vector] = 0; v(0) [vector] = v0 [vector] ; v0z > 0 and find x(τ) [vector] and v(τ) [vector], such that z(τ) = 0;  τ≠0. c) Find S. Homework Equations Euler-Lagrange equation and...