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Transforme kinetic energy in parabolical cyndrical coordinates

  1. Sep 4, 2012 #1
    1. The problem statement, all variables and given/known data

    The transformation from cartesian coordinates to cylindrical coordinates is given by:

    x = 1/2 (u2 - v2), y=uv, z=z

    2. Relevant equations

    compute the kinetic energy 1/2mv2 in parabolic cylindrical coordinates

    3. The attempt at a solution

    Any ideas??
     
  2. jcsd
  3. Sep 5, 2012 #2
    In carteesian coordinates, [itex] E = \frac{1}{2} m v^2 = \frac{1}{2} m (\dot{x}^2+\dot{y}^2+\dot{z}^2) [/itex]. You want to write this into a form with u,v and z. Maybe the chain rule would be useful: [tex] dx = \frac{\partial x}{\partial u}du + \frac{\partial x}{\partial v}dv + \frac{\partial x}{\partial z}dz [/tex]
    etc.
     
  4. Sep 5, 2012 #3
    Thank you, actually I used that one to solve the problem =)
     
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