Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Christoffel symbols examples

  1. Mar 20, 2007 #1
    i'm having a hard time computing these so could people show me several examples to help me get a better feel for them before I move on to curvature?
  2. jcsd
  3. Mar 20, 2007 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    One of the simplest examples would be to calculate the connection coefficients for the 3D Euclidean space using spherical polar coordinates. Here the line element is of the form [tex]ds^2=dr^2+r^2d\theta^2+r^2\sin^2\theta d\phi^2[/tex]. Could you try this one?

    As an aside, have you studied and Lagrangian mechanics? If so, there is a method of obtaining the connection coefficients from the Euler-Lagrange equations which is sometimes less time consuming than using the definition involving the metric tensor.
  4. Mar 20, 2007 #3
    No but i know the euler lagrage equation.
  5. Mar 20, 2007 #4


    User Avatar
    Staff Emeritus
    Science Advisor

    Maybe it's easier to just use the definition of the symbols. Try plugging in the metric coefficients and see what you get for the gammas.
  6. Mar 20, 2007 #5
    Yes but could you still show me some examples, i'm not particularly comfortable with thses symbols.
  7. Mar 20, 2007 #6


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

  8. Mar 20, 2007 #7
    It's ok I'm fine now.
  9. Mar 24, 2007 #8
    If you have Maple and GRTensor package you can calculate christoffel symbols for many metric files coming with the grtensor package and work them out yourself to exercise.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Christoffel symbols examples
  1. Christoffel Symbols (Replies: 2)

  2. Christoffel Symbol (Replies: 8)