Christoffel symbols examples

  • Thread starter Terilien
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140
0
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?
 

cristo

Staff Emeritus
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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.
 
140
0
No but i know the euler lagrage equation.
 

cristo

Staff Emeritus
Science Advisor
8,056
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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.
 
140
0
Yes but could you still show me some examples, i'm not particularly comfortable with thses symbols.
 
140
0
It's ok I'm fine now.
 
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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