Christoffel symbols examples

  • Thread starter Terilien
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  • #1
Terilien
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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?
 

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  • #2
cristo
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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.
 
  • #3
Terilien
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No but i know the euler lagrage equation.
 
  • #4
cristo
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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.
 
  • #5
Terilien
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Yes but could you still show me some examples, I'm not particularly comfortable with thses symbols.
 
  • #6
robphy
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http://www.mth.uct.ac.za/omei/gr/chap6/frame6.html
 
  • #7
Terilien
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It's ok I'm fine now.
 
  • #8
cosmicstring1
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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.
 

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