# Christoffel symbols examples

#### Terilien

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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#### cristo

Staff Emeritus
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 $$ds^2=dr^2+r^2d\theta^2+r^2\sin^2\theta d\phi^2$$. 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.

#### Terilien

No but i know the euler lagrage equation.

#### cristo

Staff Emeritus
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.

#### Terilien

Yes but could you still show me some examples, i'm not particularly comfortable with thses symbols.

Homework Helper
Gold Member

#### Terilien

It's ok I'm fine now.

#### cosmicstring1

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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