Lagrangian Definition and 1000 Threads

Homework Statement To try and relate the three ways of calculating motion, let's say you have a particle of some mass, completely at rest, then is acted on by some force, where F equals a constant, C, times time. (C*t). I want to find the equations of motion using Lagrangrian, but also Newton...

Homework Statement So, basically there is a stick, mass m and length l, that is pivoted at its top end, and swings around the vertical axis with angular frequency omega. The stick always makes an angle theta with the direction of gravity. I am told there are 2 degrees of freedom (theta...

Homework Statement for particle with lagrangian L = m/2 dx/dt^2 + fx where x is constant force, what is ScL (classical action) Homework Equations d/dt (∂L/∂(dx/dt)) = ∂L/∂x ScL = ∫m/2 dx/dt^2 + fx dt from ti to tf The Attempt at a Solution d/dt (∂L/∂(dx/dt)) = ∂L/∂x implies f =...

Homework Statement Consider the following Lagrangian: \begin{equation} L = \frac{m}{2}(a\dot{x}^2 + 2b\dot{x}\dot{y} + c\dot{y}^2)- \frac{k}{2}(ax^2 + 2bxy + cy^2)\end{equation} Assume that \begin{equation} b^2 - 4ac \ne 0 \end{equation}Find the equations of motion and examine the cases...

I have been looking at the problem of 2 point masses connected by a spring in polar coordinates. The problem is solved using the center of mass coordinate R and the relative coordinate r where M=total mass and m=reduced mass. The Euler-Lagrange equations then give equations for P(a vector) and...

Hi everyone! I've been thinking about a certain problem for a while now. And that is a Lagrangian formulation of Newtonian gravity. I know there is a Lagrangian formulation for general relativity. But I was hoping to find a Lagrangian for Newtonian gravity instead (for some continuous mass...

Hello, this is probably one of those shoot yourself in the foot type questions. I am going through Landau & Lifshits CM for fun. On page 7 I do not understand this step: L' = L(v'^2) = L(v^2 + 2 \vec{v} \cdot \vec{\epsilon} + \epsilon^2) where v' = v + \epsilon . He then expands the...

Homework Statement Build the lagrangian of a set of N electric dipoles of mass m, length l and charge q. Find the equations of motion. Find the corresponding difference equations. Homework Equations Lagrange function L=T-V Lagrange's equations \frac{d}{dt}\left(\frac{\partial L}{\partial...

The full Lagrangian for electrodynamics ##\mathcal{L}## can be expressed as ##\mathcal{L}=\mathcal{L}_\textrm{field}+ \mathcal{L}_\textrm{interaction}+\mathcal{L}_\textrm{matter}##. Practically every textbook on relativity shows that...

Can you please tell me whether I am right or wrong? Lagrangians are scalars. They are NOT invariant under coordinate transformations[ the simplest example is when you have a gravitational potential(V=mgz) and you translate z by "a"(some number)...

If you don't have any charges or currents, the electromagnetic Lagrangian becomes ##\mathcal{L}=-\frac{1}{4}F_{\alpha\beta}F^{\alpha\beta}##. The standard way to derive Maxwell's equations in free space is to replace ##F_{\alpha\beta}## by ##\partial_\alpha A_\beta -\partial_\beta A_\alpha## and...

The question is that a mass m of weight mg is attached to a fixed point by a light linear spring of stiffness constant k and natural length a. It is capable of oscillating in a vertical planne. Let θ be the angle of the pendulum wrt to the vertical direction, and r the distance between the mass...

The Lagrangian for a point particle is just L=-m\sqrt{1-v^2}. If instead we had a continuous distribution of matter, what would its Lagrangian density be? I feel that this should be very easy to figure out, but I can't get a scalar Lagrangian density that reduces to the particle Lagrangian in...

Hi there, I am reading about Lagrangian mechanics. At some point the difference between the temporal derivative of a variation and variation of the temporal derivative is discussed. The fact that the two are the same is presented in the book I am reading as a rule, commutativity, and...

I have been reading Lagrangian from Classical Mechanics by John R. Taylor. I have adoubt in a derivation which invloves differential calculus. I have attached snapshot of the equation , can someone please explain. Here y,η are functions of x but α is s acosntant. Please let me know if I...

What is the Lagrangian of interaction of photon and spin zero charge scalar?The vertex of photon and spin 1/2 charge fermion is proportional with e multiplied vertor gamma matrix,but I do not know what is the vertex of photon and charge scalar.I hear that a vertex is proportional with polynomial...

This thread is supposed to be a continuation of the discussion of this thread: (1) https://www.physicsforums.com/showthread.php?t=88570. The previous thread was closed but there was a lot of things I did not understand. This is also somewhat related to a recent thread I created: (2)...

I recently posted another thread on the General Physics sub forum, but didn't get as much feedback as I was hoping for, regarding this issue. Let's say I have two Lagrangians: $$ \mathcal{L}_1 = -\frac{1}{2}(\partial_\mu A_\nu)(\partial^\mu A^\nu) + \frac{1}{2}(\partial_\mu A^\mu)^2 $$ $$...

Hey everyone, I wasn't really sure where to post this, since it's kind of classical, kind of relativistic and kind of quantum field theoretical, but essentially mathematical. I'm reading and watching the lectures on Quantum Field Theory by Cambridge's David Tong (which you can find here), and...

Question 1 When I take the derivatives of the Lagrangian, specifically of the form: \frac{\partial L}{ \partial q} I often find myself saying this: \frac{\partial \dot{q}}{ \partial q}=0 But why is it true? And is it always true?

Hello, I understand the classical Lagrangian which follows the Principle of Least Action(A) A=∫L dt But what is Lagrangian density? Is it a new concept? A=∫Lagrangian density dx^4 Here 4 is the four vector? One time-like and 3 space-like co-ordinates? QFT uses Lagrangian to...

Homework Statement A Particle of mass m is threaded on a frictionless rod that rotates at a fixed angular frequency Ω about a vertical axis. A spring with rest length Xo and spring constant k has one of it's ends attached to the mass and the other to the axis of rotation. Let x be the length...

Homework Statement While doing a problem I have found the Lagrangian to be L=\frac{1}{2}m \dot{r}^2 \left( 1 + 4a^2r^2 \right) + \frac{1}{2}mr^2 \dot{\theta}^2 -mgar^2. I have also shown that the angular momentum l is constant and is equal to l=mr^2 \dot{\theta}. I want to calculate the energy...

Homework Statement Consider a bead of mass m moving on a spoke of a rotating bicycle wheel. If there are no forces other than the constraint forces, then find the Lagrangian and the equation of motion in generalised coordinates. What is the possible solution of this motion?Homework Equations...

Homework Statement [/b] The attempt at a solution[/b] I have done the first bit but don't know how to show that phi(r,t) is a solution to the equation of motion.

Hello fellow PF members I was wondering how one would go about finding the lagrangian of a problem like the following: A particle is constrained to move along the a path defined by y = sin(x). Would you simply do this: x = x y = sin(x) x'^2 = x'^2 y'^2 = x'^2 (cos(x))^2...

Hello, I have a very basic question: Degrees of freedom for a particle describes the formal state of a physical system. Like a particle in 3 dimension space has 3 co-ordinates and if it moves in 3 velocity components, then it has 6 degrees of freedom. Lagrangian also measures this, right?

Homework Statement I'm asked to solve the typical intro level box on an inclined plane problem but I need to do it using the lagrangian. My difficulty with it is that the axis I am required to use are not the typical axes used when solving this using Newtonian mechanics. Instead of the...

This is probably a minor point, but I have seen in some QFT texts the Euler-Lagrange equation for a scalar field, \partial_{\mu} \left(\frac{\delta \cal{L}}{\delta (\partial_{\mu}\phi)}\right) - \frac{\delta \cal L}{\delta \phi }=0 i.e. \cal L is treated like a functional (seen from the...

Homework Statement I don't know why I'm having trouble here, but I want to show that, if we let t = t(\theta) and q(t(\theta)) = q(\theta) so that both are now dependent coordinates on the parameter \theta , then L_{\theta}(q,q',t,t',\theta) = t'L(q,q'/t',t) where t' =...

Homework Statement Consider the following Lagrangian in Cartesian coordinates: L(x, y, x', y') = 12 (x^ 2 + y^2) -sqrt(x^2 + y^2) (a) Write the Lagrange equations of motion, and show that x = cos(t); y =sin(t) is a solution. (b) Changing from Cartesian to polar coordinates, x = r...

In Lagrangian mechanics, the Euler-Lagrange equations take the form $$\frac{\partial L}{\partial x} = \frac{\mathbb{d}}{\mathbb{d}t}\frac{\partial L}{\partial \dot{x}}$$ From this, we can define the left side of the equation as force, and by carrying out the actual derivative, we get $$F =...

a particle of mass m is attracted to a center force with the force of magnitude k/r^2. use plan polar coordinates and find the Lagranian equation of motion. so i thought for the kinetic energy it would be.. K=\frac{1}{2}m(r2\dot{θ}2) since v2 = r2\dot{θ}2 but no.. the kinetic energy...

hi, silly question but would someone please show me how \frac{∂L}{∂q}=\dot{p}? L being the lagrangian, p being the momentum, and q being the general coordinate.

Hi Can somebody please explain fundamentally what is the difference between these two methods of modelling contact interfaces? I would prefer a more qualitative explanation (physics concept based ) rather than a more mathematical description.

Homework Statement A bead of mass m slides under gravity on a smooth rod of length l which is inclined at a constant angle ##\alpha## to the downward vertical and made to rotate at angular velocity ##\omega## about a vertical axis. The displacement of the bead along the rod is r(t)...

Hi all, I've been playing around with spin 1/2 Lagrangians, and found the very interesting Fierz identities. In particular for the S x S product, (\bar{\chi}\psi)(\bar{\psi}\chi)=\frac{1}{4}(\bar{\chi} \chi)(\bar{\psi} \psi)+\frac{1}{4}(\bar{\chi}\gamma^{\mu}\chi)(\bar{\psi}\gamma_{\mu}...

Dear All, To give a background about myself in Classical Mechanics, I know to solve problems using Newton's laws, momentum principle, etc. I din't have a exposure to Lagrangian and Hamiltonian until recently. So I tried to read about it and I found that I was pretty weak in coordinate...

Homework Statement This is the problem: http://i.imgur.com/OJyzfhz.png?1 Homework Equations $$\frac{dL}{dq_i}-\frac{d}{dt}\frac{dL}{d\dot{q_i}}=0$$ $$ L=\frac{1}{2}mv^2-U(potential energy)$$ The Attempt at a Solution This is my attempt at question A): http://i.imgur.com/IeJVGm3.jpgDoes...

Homework Statement I need some help understanding a derivation in a textbook. It involves the Lagrangian in generalized coordinates. Homework Equations The text states that generalized coordinates {q_1, ..., q_3N} are related to original Cartesian coordinates q_\alpha = f_\alpha(\mathbf r_1...

Homework Statement Consider the Lagrange Polynomial approximation p(x) =\sum_{k=0}^n f(x_k)L_k(x) where L_k(x)=\prod_{i=0,i\neq k}^n \frac{x-x_i}{x_k-x_i} Let \psi(x)=\prod_{i=0}^n x-x_i. Show that p(x)=\psi(x) \sum_{k=0}^n\frac{f(x_k)}{(x-x_k)\psi^\prime(x)} Homework Equations None...

I tried to verify that the SYM lagrangian is invariant under SUSY transformation, but it turned out there is a term that doesn't vanish. The SYM lagrangian is: \mathscr{L}_{SYM}=-\frac{1}{4}F^{a\mu\nu}F^a_{\mu\nu}+i\lambda^{\dagger a}\bar{\sigma}^\mu D_\mu \lambda^a+\frac{1}{2}D^a D^a the...

Hello, Does anyone know what "induced gravity" is and where can one read (something not too technical) about it? I am trying to understand how a system with zero Lagrangian has something to do with gravity. Could someone explain perhaps? Thanks

I am learning Hamiltonian and Lagrangian mechanics and looking for a book that starts with Newtonian mechanics and then onto Lagrangian & Hamiltonian mechanics. It should have some historical context explaining the need to change the approaches for solving equation of motions. Also it should...

Hello! I've read thousand of explanations about how q and q-dot are considered independent in the Lagrangian treatment of mechanics but I just can't get it. I would really appreciate if someone could explain how is this so and (I've seen something about an a-priori independence but I couldn't...

In a two-body solution ( Kepler Problem) how do you find the Lagrangian, L, if the position vector is: x = (v_x * t + x_0, v_y * t + y_0, v_z * t + z_0) Action from Wikipedia is: S = \int_{t_1}^{t_2} L * dt

How are the Hamiltonian and Lagrangian different as far as preserving symmetries of a theory? Peskin and Schroeder write that the path integral formalism is nice because since it's based on the action and Lagrangian it explicitly preserves all the symmetries, but I'm wondering how/why the...

A few doubts regarding lagrnagian method to deal with motion of particles: 1) It seems like a heuristic method of solving for motion of a particle. In Newtonian mechanics, you carefully consider all the forces and find out the particle's motion. In this, based on intuition you guess the...

Homework Statement I am studying inflation theory for a scalar field \phi in curved spacetime. I want to obtain Euler-Lagrange equations for the action: I\left[\phi\right] = \int \left[\frac{1}{2}g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi + V\left(\phi\right) \right]\sqrt{-g} d^4x Homework...

Homework Statement Consider the following Lagrangian of a relativistic particle moving in a D-dim space and interacting with a central potential field. $$L=-mc^2 \sqrt{1-\frac{v^2}{c^2}} - \frac{\alpha}{r}\exp^{-\beta r}$$ ... Find the velocity v of the particle as a function of p...