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Transforme kinetic energy in parabolical cyndrical coordinates

  • #1

Homework Statement



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

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

Homework Equations



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

The Attempt at a Solution



Any ideas??
 

Answers and Replies

  • #2
938
9
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.
 
  • #3
Thank you, actually I used that one to solve the problem =)
 

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