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Lagrangian of a particle moving in a cone

  1. May 17, 2012 #1
    1. The problem statement, all variables and given/known data

    naaxv.jpg

    2. Relevant equations

    Euler-Lagrange equations of motion

    3. The attempt at a solution

    Part a): Particle must move on surface (one constraint). Number of generalised coordinates = 3N - K where N = number of particles and K = constraints. Therefore 2 generalised coordinates are needed.

    Part b): Is the Lagrangian obtained using the symmetric axis of the cone as the vertical plane for the longitude phi?

    Part c): L independent of t -> Hamiltonian is constant (Total energy conserved)
    : L independent of phi -> Angular momentum is conserved

    Part d) and e) are troublesome, any help is appreciated.
     
  2. jcsd
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