Lagrangian mechanics Definition and 193 Threads

Hey everyone, So I'm just looking around to get a hold of some lagrangian mechanics for the GRE's coming up. Is the lagrangian always dealing with energy? Basically there was a problem I encountered with trying to find the lagrangian of a rolling ball in some setup, and once I knew that it was...

Homework Statement See image (I think I forgot to rotate it, careful with your necks!): http://img600.imageshack.us/img600/7888/p1000993t.jpg The system consists of 2 point masses joined by a rigid massless bar of length 2l, which can rotate freely only in the z-x plane. The center of...

According to my CM text, Lagrangian Mechanics can be used to derive Newton's laws. We define the Lagrangian as L=T-V. Now, how do we know what T is? Is it defined to be 1/2mv^2? The only way I know how to derive that is using the work energy theorem which feels like 'cheating' since I am...

Homework Statement Find the Lagrangian and solve for the equations of motion. (see attached image)Homework Equations Euler-Lagrange's equation.The Attempt at a Solution I just wanted to check if I picked the right generalized coordinates. The pic shows what I think is called a Thompson-Tait...

Does anyone have any tips on how to properly determine the degrees of freedom in simple mechanical systems? I've done many problems but I often encounter a new one (or make one up myself) where I can't seem to get the proper number of generalized coordinates down right. Things like coupled beads...

Euler Lagrange Equation : if y(x) is a curve which minimizes/maximizes the functional : F\left[y(x)\right] = \int^{a}_{b} f(x,y(x),y'(x))dx then, the following Euler Lagrange Differential Equation is true. \frac{\partial}{\partial x} - \frac{d}{dx}(\frac{\partial f}{\partial y'})=0...

Homework Statement A cylinder of mass m and radius R rolls without slipping down a wedge of mass M. The wedge slides on a frictionless horizontal surface. The angle between the wedge's hypotenuse & longest leg (which lies on the frictionless ground) is beta. The wedge's hypotenuse DOES have...

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, 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...

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...

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...

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 =...

I am having a lot of trouble conceptually understanding this issue in Lagrangian mechanics: I have an airfoil which is immersed in incompressible flow: it has two degrees of freedom: a rotation: alpha and a pitching (up down) motion: h. Now the lift is due to both alpha and the first derivative...

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...

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...

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...

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)...

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 +...

Hello, I am just starting Lagrangian mechanics and on a conservation problem but I am stuck. I have part of the solution (i think) but I am not sure how to complete it. Homework Statement In an infinite homogeneous plane. Find all the components of momentum and angular momentum that are...

Homework Statement A massless spring (spring constant k) is attached to the ceiling. It is free to move only in the y-direction. A homogenous bar of mass m and length l is attached from its other end to the lower end of the spring, and the bar is free to move on the xy-plane. A fancy...

Homework Statement Here's a little diagram I whipped up in paint: http://img83.imageshack.us/img83/7625/diagramcj4.th.jpg Sorry about my sucky art skills. The wiggly line is a spring with spring constant mk and natural length d. The actual length of the spring is y. The two masses to...

Homework Statement A particle of mass m moves in a potential of the form U(r) = (1/2)kr^2 k = const greater than zero 1) Determine the possible orbits r = r(theta) and show that they are closed 2) Solve the equations of motion (although it is sufficient to derive the time...

the problem formulation is the next: there is a manifold N of dimension n. inside N there is another submanifold M of dimension m\leq n. let \{q_i\} be a coordinate system over N such that q_i = 0 for i = m+1,...,n if the point given by \vec{q} is in M. let L(\vec{q}) be a lagrangian...

I'm stuck on a problem with lagrangian mechanics. Here's the problem; One end of a rod slides along a vertical pole while the other end slides a long a horizontal pole. At the same time a bean slides a long the rod. Find the lagrangian for the system. And this is what I worked...

Homework Statement A simple pendulum (mass M and length L) is suspended from a cart (mass m) that can oscillate on the end of a spring of force constant k. Write the Lagrangian in terms of the two generalized coordinates x and \phi, where x is the extension of the spring from its...

can someone post a really good e-book of lagarangian mechanics(ofcourse for newbies:smile:) if thsi is not the right forum for such a question then sorry:cry:

I'm trying to understand something that's coming from my Marion & Thornton (4th edition 1995 on p. 264 in a section titled "Conservation Theorems Revisited"). The topic is conservation of energy and introduction of the Hamiltonian from Lagrange's equations. We're told that the Lagrangian...

Is it possible to find a lagrangian for a system with a varible mass and have a vaild solution when you are complete? For instance, if I have a chain falling over the edge of a table or a rocket how would one approach this.Example of my thinking: For a chain falling over a table, if we assume...

I must solve the following two coupled EDOs in the context of a Lagrangian mechanics problem (a rigid pendulum of length l attached to a mass sliding w/o friction on the x axis). The problem statement does not mention that we can make small angle approximation. It says "find the equations of...

I have two point masses that are connected by a massless inextensible rope of length l which passes through a small hole in a horizontal plane. The first point mass moves without friction on the plane while the second point mass oscillates like a simple pendulum in a constant gravitational field...

I, beginner to Lagrangian mechanics, was reading Hand and Finch and got stuck with a concept.it was the development to lagrangian formulation by treating a problem, first in Newtonian way, then using virtual work consideration and finally, the Lagrangian way,the last is still beyond my read...

In the theory of Lagrangian mechanics, it is said that given a system of particles, write the Lagrangian T-U in cartesian coordinates, convert to generalized coordinates, solve the Lagrange equations, and re-convert to cartesian if you feel like it. But there's something weird going on, and...

The Lagrangian of a aprticle of charge q and mass m is given by L = \frac{1}{2} m \dot{r}^2 - q \phi(r,t) + \frac{q}{c} r \bullet A(r,t) a) determine the Hamiltonain function H(r,p) (in terms of r and its conjugate momentum p) and explain waht conditions the electric and mangetic field...

consider a bead of mass m constrained to move on a fricitonless wire helix whose equations in cylindrical polar coords is z = a phi where a is some constant the bead is acted upon by a force which deends on the distance from the cneter only. Formulate the problem using s the distance along...

Hello I'm having a bit of trouble with analysing some of the coupled oscillator questions in terms of the energy functions. Here is a coupled oscillator diagram: http://img356.imageshack.us/img356/28/coupledlagr4fx.png Now for this one my main problem is that I don't know how to come up...

"There is some freedom as to what we choose for the Lagrangian in a given problem: We can add a constant, multiply by a constant, change the time scale by a multiplicative constant, or add the total time derivative ... Any of these transformations will lead to a Lagrangian that is perfectly...

Hi! I want to calculate the movement of the rod in the picture, but I don't know how to put up the Lagrangian for the problem. I have the Shear modulus, \mu, for the material and M>>m and \theta = 0. I need the Lagrangian and from there on I think I can manage with the calculations myself...

Hi, I would like some help in proving the following: Consider the action for a particle in a potential U. Show that an extremum path is never that of a local maximum for the action. I think what I have to do is look at the second derivative of the action integral. Then I should somehow...

Dear friends, Well, I’ve got a problem to solve but I’m not going to ask you to do it for me. Instead, what I need is an explanation of what I am doing wrong. The problem is as follows: we have a rod of mass m and length l hanging of a rail (don’t know how to call it). It moves as the...

Dear friends, After having studied thermodynamics for some months as well as Lagrangian mechanics, I'm trying to find a relationship between the Hamiltonian, Lagrangian, conjugated potentials etc. and thermodynamic potentials (such as Gibbs free energy, Enthalpy etc.). I mean, they may...

I have seen that Lagrange's equations are some times derived from Hamilton's principle. This makes me wonder what the historical development of these ideas was. Hamilton lived in the nineteenth century while Lagrange lived in the eighteenth century. The principle that minimizes the integral of...