1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor

    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!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Kinetic Energy in Spherical Coordinates? (For the Lagrangian)
  1. Spherical Coordinates (Replies: 2)