Lagrangian Definition and 1000 Threads

Homework Statement A particle moves so that \vec{x} \equiv [x_0 exp(2t^2), y_0 exp(-t^2), z_0 exp(-t^2)] . Find the velocity of the particle in terms of x_0 and t (the LAgrangian description) and show it can be written as \vec{u} \equiv (4xt, -2yt, -2zt), the Eulerian description...

Can we use the method of Lagrangian equation in the very high velocity system and how to use it? Thank you.

Homework Statement If I consider a 3 dimensional problem related to a spring pendulum (a mass attached to the end of a spring of constant k and the other end of the spring remains fixed) and I want to find the equations of motion of the mass (for several initial conditions), what system of...

Hi, so today in maths we defined the Lagrangian as L = T-V and stated Hamilton's Principle, which says that the actual path of a conservative system is the one which minimises the action A(q)=\int^{t_{2}}_{t_{1}}L dt. I'm a bit confused about this. What does the action represent in physical...

Hi, I am going through my notes trying to get things straight in my head and something is confusing me. I also have the feeling it will turn out not to be very complicated, which is why I am a bit frustrated with this. I know that there is something used in general relativity called the...

Homework Statement A block of mass m moves on a horizontal, frictionless table. It is connected to the centre of the table by a massless spring, which exerts a restoring force F obeying a nonlinear version of Hooke's law, F = -kr + ar^3 where r is the length of the spring. Show that the...

Homework Statement Consider the spherical pendulum. In other words a particle with mass m constrained to move over the surface of a sphere of radius R, under the gravitational acceleration \vec g. 1)Write the Lagrangian in spherical coordinates (r, \phi, \theta) and write the cyclical...

Hello everyone, I have a problem with 4 degrees of freedom, 2 of which are superfluous. My goal is to derive the equations of motion. I have derived the equations connecting the superfluous DoFs with the independent ones, however they are nonlinear and interlaced, which means that I cannot...

Hi guys, I have a question about finding a lagrangian formulation of a theory. If I have a system for which I know the equations of motion but not the form of the lagrangian, is it possible to find the lagrangian that will give me those equations of motion? Is there a systematic way of doing...

I don't have the books in front of me so I only use my memory. According to my professor and if I remember well, Landau and Lifgarbagez, the Lagrangian of an isolated particle can in principle depend on \vec q, \vec \dot q and t. Therefore one can write L(\vec q, \vec \dot q , t). With some...

Homework Statement The main problem is that I do not understand the problem. Here it is: A particle describes a one-dimensional motion under the action of a conservative field: \ddot r =-\frac{dU(r)}{dr}. Consider now the following coordinates transformation: r=r(q,t). Demonstrate that the...

Homework Statement I challenged myself with a problem I invented, but I'm stuck. Consider a 1 dimensional problem consisting of 3 masses, each one separated by a spring. So that from the left to the right of my sketch we have m_1, a spring (k_1 with natural length l_1), m_2, another spring...

Homework Statement The problem can be found in L&L's book "Mechanics" in the end of the first chapter. (See the last picture of page 12 of http://books.google.com.ar/books?id=QkYRDGH5tg0C&printsec=frontcover&dq=inauthor:%22Lev+Davidovich+Landau%22&cd=2#v=onepage&q&f=false ). The mass m1 is...

Let's say that L=((1/2)m*v^2-V(x))*f(t), or something similar. What are the equations of motion? For time independent it should be: (d/dt) (dL/dx_dot)=dL/dx . Using this I get m\ddot{x}+m f_dot/f x_dot+dV/dx=0. Is this right? I keep thinking about the derivation of the equations and it...

Homework Statement From pages 124-125 in edition 3. This is about the restricted three body problem (m3 << m1,m2) http://img718.imageshack.us/img718/7012/3bdy.jpg Homework Equations L = T-V Euler-Lagrange equations The Attempt at a Solution I'm interested in m3, the...

Homework Statement A system with only one degree of freedom is described by the following Hamiltonian: H = \frac{p^2}{2A} + Bqpe^{-\alpha t} + \frac{AB}{2}q^2 e^{-\alpha t}(\alpha + Be^{-\alpha t}) + \frac{kq^2}{2} with A, B, alpha and k constants. a) Find a Lagrangian...

i have some question about lagrangian ...here are those 1) what is the physical meaning of L=0 .. from wiki ..i have found .."The Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system." that means when L=0 ..the system has no dynamics ..as far as i...

Homework Statement Rather than solve the double pendulum problem with two masses in the usual way. Instead express the coordinates of the second mass, in terms of the coordinates of the mass above it. $ x2=x_1+\xi = L_1Sin[\theta]Cos[\phi]+L_2Sin[\alpha]Cos[\beta]$\\ $ y2=y_1+ \eta =...

Hello, I'm trying to follow an argument in Landau's Mechanics. The argument concerns finding the Lagrangian of a free particle moving with velocity v relative to an inertial frame K. (of course L=1/2 mv^2, which is what we have to find). I'll state the points of the argument: (0) It has...

I've seen in textbooks before, there if there were monopoles, Maxwell's equations would look more "symmetric" between the E and B fields. Such that (in cgs units): \begin{align*} \nabla \cdot \mathbf{E} &= 4 \pi \rho_e \\ \nabla \cdot \mathbf{B} &= 4 \pi \rho_m \\ -\nabla \times...

Homework Statement A particle is confined to move on the surface of a circular cone with its axis on the vertical z axis, vertex at the origin (pointing down), and half-angle a. (a) Write the Lagrangian L in terms of the spherical polar coordinates r and ø. (b) Find the two equations of...

Consider a one dimensional gauge theory where the field has mass. The term, m^{2}A^{\mu}A_{\mu} is the conventional mass term. What if you find terms in your Unified Field Theory lagrangian of the form M_{\mu\nu}A^{\mu}A^{\nu} ? In this case M_{\mu\nu} is constant. When it is...

Homework Statement Consider a particle of mass m sliding under the influence of gravity, on the smooth inner surface of the hyperboloid of revolution of equation x^2 + y^2 = z^2 -a^2 where (x,y,z) are the Cartesian co-ordinates of the particle (z > 0) and (a > 0) is a constant. The...

Can you please tell me some resource or link that has the lagrangian for SO(10) GUT written explicitely term by term? Any version of SO(10) GUT is fine(I mean based on the way the symmetry is broken)

Hello. I am having trouble realizing the following relation holds in Lagrangian Mechanics. It is used frequently in the derivation of the Euler-Lagrange equation but it is never elaborated on fully. I have looked at Goldstein, Hand and Finch, Landau, and Wikipedia and I still can't reason...

Hi All, I am trying to derive the equation of motion from a Lagrangian with a gauge fixing term, and I think get quite close to the result, but am missing some steps somewhere. These indices and notation is new to me, so please feel free to bring any mistakes to my attention. So the...

The hermiticity of Hamiltonian comes up as a result of requiring real energy eigenvalues and well-defined inner-product for correlation amplitudes. In the corresponding Lagrangian picture (path-integral), I am not clear about the explicit restriction that the above hermiticity of Hamiltonian...

Does anyone know how long SOHO and ACE took to get to the L1 lagrangian point. It is in average 1.496 million km away, I am wondering how fast a human space flight servicing mission would take. Also if it is possible to send it for a long mission seeing that the radiation dosage increases and...

hi everyone! I have just posted a thread which was about the equivalent lagrangian. and I think I have another problem with it too! again in section 11.6 d'inverno, it is said that if you use equation 11.37 then you can achive (∂L ̅)/(∂g_(,c)^ab )=Γ_ab^c-1/2 δ_a^c Γ_bd^d-1/2 δ_b^c...

Hi everyone! again problem with d'inverno's equation! ok let me see, in chapter 11 section 11.6, it is said that (∂L ̅)/(∂g^ab )=Γ_ac^d Γ_bd^c-Γ_ab^c Γ_cd^d as we see at first if you derive (∂L ̅)/(∂g^ab ) from equation 11.37 you can have the above result. but my professor said it's...

Dear everyone can anyone help me with the euler lagrange equation which is stated in d'inverno chapter 11? in equation (11.26) it is said that when we use the hilbert-einstein lagrangian we can have: ∂L/(∂g_(ab,cd) )=(g^(-1/2) )[(1/2)(g^ac g^bd+g^ad g^bc )-g^ab g^cd ] haw can we derive...

Hi! I´m a senior high school student and I´m doing a school project about the conservation laws. I enjoy physics very much and I come asking you for advice. This is not a homework question. After doing most of my work for the school project, I´ve been told that you can get a deeper knowledge...

In general what does a Lagrangian for a system consisting of interacting fields and particles look like? It can't be, for example, L=\sum{\frac{1}{2}mv_j^2+A(x_j)\inner v_j} That would be for a system of particles in a fixed, i.e. "background", field. I'm interested in how we can mix...

Hi. There is just this one thing in mechanics which is lagrangian that I just simply can't grasp physically. I'm taking a mechanics course I simply do not understand what the lagrangian is. There is calculus of variations (at least a tiny but of it) a bit of geodesics and the least action...

What are the dimensions of a scalar field \phi ? The Lagrangian density is: \mathcal L= \partial_\mu \phi \partial^\mu \phi - m^2 \phi \phi So in order to make all the terms have the same units, you can try either: \mathcal L=\frac{\hbar^2}{c^2} \partial_\mu \phi \partial^\mu \phi -...

Hi, Hope someone can help me clear up this question. I know the answer but I am unsure of the reasoning behind it, so here it is: Question:A simple pendulum of mass m and length l hangs from a trolley of mass M running on smooth horizontal rails. The pendulum swings in a plane parallel to the...

I was just doing a simple 2-body Newtonian gravitation problem. The force on each mass is: f=\frac{G m_1 m_2}{r^2} and the integral of the force wrt r is: \int \! f \, dr = -\frac{G m_1 m_2}{r} So, since there are two forces in the system, one on each object, I had assumed that there would...

Which textbooks formulate Quantum Mechanics (or, for that matter, QFT) in Langrangian terms?

I'm trying to solve a problem for a relativistic electron in an external magnetic field with vector potential \vec A using the Lagrangian \mathcal L = -mc^2 / \gamma - e \vec v \cdot \vec A in cylindrical coordinates. But isn't this DREADFULLY TERRIBLE, since when I try to compute...

In J.D. Jackson's Classical Electrodynamics, an argument is made in support of the assertion that the relativistic Lagrangian \mathcal L for a free particle has to be proportional to 1/\gamma. The argument goes something like this: \mathcal L must be independent of position and can therefore...

A uniform ladder of mass M and length 2L is leaning aainst a frictionless vertical wall with its feet on a frictionless horizontal floor. Initially the stationary ladder is released at an angle \theta_{0} = 60o to the floor. Assume that the gravitation field g acts vertically downward. 1)...

Homework Statement Find the shape of a tunnel drilled through the Moon such that the travel time between two points on the surface of the Moon under the force of gravity is minimized. Assume the Moon is spherical and homogeneous. Hint: Prove that the shape is the hypercycloid x(θ) = (R...

Dear all, could please give my some links or references to material that justifies the mathematical and physical reasons for introducing these two formalisms in mechanics? Thanks. Goldbeetle

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 ?