1. K


    This is just a made up problem of a fake trajectory to help me understanding the Lagrangian I am trying to compute the action of this graph if m = 1 then I assume that the Lagrangian is the integral of T-V = 1 - 0.5t^2 for 0 <= t < 1 and T = 1.5 - (.5 - 0.5t^2) for 1 < t <= 2. This is...
  2. K

    Trying to get my head around the Lagrangian

    In the calculus of variation they set up the problem as action S where and In the case of finding the shortest distance between two points this makes sense but in the case of finding the path of least time as in a roller coaster shaped like a e Brachistochrone I am not getting why...
  3. B

    Stress energy tensor transformation

    Show that if you add a total derivative to the Lagrangian density L \to L + \partial_\mu X^\mu, the energy momentum tensor changes as T^{\mu\nu} \to T^{\mu\nu}+\partial_\alpha B^{\alpha\mu\nu} with B^{\alpha\mu\nu}=-B^{\mu\alpha\nu}. (Note: the Lagrangian can depend on higher order derivatives...
  4. T

    Mechanics II: Hamiltonian and Lagrangian of a relativistic free particle

    The Problem: I am given the Hamiltonian of the relativistic free particle. H(q,p)=sqrt(p^2c^2+m^2c^4) Assume c=1 1: Find Ham-1 and Ham-2 for m=0 2: Show L(q,q(dot))=-m*sqrt(1-(q(dot))^2/c^2) 3: Consider m=0, what does it mean? Equations Used: Ham-1: q(dot)=dH/dp Ham-2: p(dot)=-dH/dq...
  5. K

    Is "Action" a contrived concept to make the Lagrangian work?

    See (attached) how the Lagrangian really was only formulated for T (kinetic energy) but by assuming conservative forces only they were able to do some hocus pocus and invent some terms (namely the time derivative of the potential) which must be zero for conservative forces so that they could...
  6. K

    Derivation of Lagrangian

    I am working through the derivation of the lagrangian but don't get this step: \frac{\partial T}{\partial \dot{q}}=\sum_{i=1}^N m_i \mathbf{\dot{r}}_i \cdot \frac{\partial \mathbf{\dot{r}_i}}{\partial \dot{q}} =\sum_{i=1}^N m_i \mathbf{\dot{r}}_i \cdot \frac{\partial \mathbf{r}_i}{\partial q}...
  7. K

    why does the Lagrangian have this form?

    In this video set to play at the right position: 3apIZCpmdls It seems as if he comes up with the formula: \delta A =\frac{\delta \mathcal{L} }{\delta x } - \frac{d}{dt} \frac{\delta \mathcal{L}}{\delta \dot{x}} However his justification seems to be that adding d/dt on the lagrangian...
  8. D

    Lagrangian Problem

    A bar of soap of mass m rests on a horizontal frictionless plate at time t = 0 at a distance of r from the point at which the plate is fixed. The plate is then lifted up at one end with the other end anchored to the ground, such that the plate moves in an arc about this point with constant...
  9. M

    SU(4) symmetry and diagonalising mass term in Lagrangian

    We have the SU(4) global symmetry of the theory. If we have an anti-symmetric tensor with two indices and write all the invariant mass terms (quadratic in field) we can diagonalise this mass term in Lagrangian with decomposing our tensor into linear combination of self-dual and anti self-dual...
  10. K

    Lagrangian Mechanics - metric tensor

    I am trying to follow the derivation of the Noether's theorem with respect to a complex wave on a guitar string. My text obtains the Lagrangian: [TEX]\mathcal{L}=\frac 12 (\partial_\mu \chi^*)(\partial^\mu \chi)[\TEX] In deriving this Lagrangian density in classical mechanics is the...
  11. K

    Lagrangian for a field

    Can anyone tell me where the lagrangian in this equation comes from? I.e. whay physical process has a Lagrangian like this? {vertical-align:15%;}
  12. S

    find the global symmetry of the lagrangian

    Hi, this is my first post so excuse me if i use this pseudo latex syntax to write the formula, but it should be clear. However going to the point: What's the global symmetry of this lagrangian? L= ( d_{mu} phi_i )( d_{mu} phi_i ) -1/2 (phi_i M_{ij} phi_j) - g (phi_i)^2 (phi_j)^2 ( s_1 0...
  13. Black

    Find the lagrangian

    The springs are without being deformed and they are ideal and located horizontally, the mass center of the kart is located in a "b" height of the center "o." The thread is ideal (of worthless mass) and "m" (the one which is below and you can't see that well) oscilates in the plane. Find the...
  14. B

    Lagrangian density of linear elastic solid

    I need the general expression for the lagrangian density of a linear elastic solid. I haven't been able to find this anywhere. Thanks.
  15. P

    Finding the lagrangian of a slipping ladder

    The problem statement : A uniform ladder of mass m and length 2a rests with one end on a smooth horizontal floor and the other end against a smooth vertical wall.The ladder is initially at rest and makes an angle alpha with the horizontal. Determine the lagrangian function for the ladder. If...