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Lagrangian and symmetry

  1. Sep 7, 2014 #1
    1. The problem statement, all variables and given/known data

    the question is that there is a particle in 3 spatial Euclidean dimensions in cylindrical coordinates.
    I want to find a symmetry for the lagrangian if the potential energy is function of r and k.theta+z
    V=V(r,k.theta+z)


    2. Relevant equations

    k is constant
    L=T-V
    T is kinetic energy
    3. The attempt at a solution
    i tried to find translational symmetry
    r --> r+s
    theta --> theta-s/k
    im not sure any help please ?
     
  2. jcsd
  3. Sep 8, 2014 #2

    vanhees71

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    Science Advisor
    2016 Award

    I'm not through with checking this example, but it looks as if it could be a good idea to use
    [itex]r[/itex], [itex]\theta[/itex], and
    [tex]u=k \theta + z[/tex]
    as the generalized variables and then perform the Lagrangeformalism. It's easy to see that with this choice of variables you make use of the very symmetry you've already identified!
     
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