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Kinetic Energy in Spherical Coordinates? (For the Lagrangian)

  1. Oct 22, 2011 #1
    I'm doing a Lagrangian problem in spherical coordinates, and I was unsure how to express the kinetic energy, so I looked it up and wiki states it should be this:


    Which would give me the correct answer, but I'm unsure how one would derive that expression. Can someone explain it? You don't necessarily have to do all the work out, just an explanation of the steps would help greatly.

  2. jcsd
  3. Oct 22, 2011 #2


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    The conversion to spherical coordinates is

    x = r sin θ cos φ
    y = r sin θ sin φ
    z = r cos θ

    Plug these into the expression for kinetic energy: T = ½m(x·2 + y·2 + z·2) and simplify.
  4. Oct 22, 2011 #3
    Ok I'll try it! That looks simple... doh!
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