How Do You Derive Christoffel Symbols from These Equations?

[m.medhat]

hello,
i have a question about christoffel symbols . if we have :-
[PLAIN]http://www.tobikat.com
how can I derive these equations :-
[PLAIN]http://www.tobikat.com
please i want the answer be clear .


with very thanks...

 

[Altabeh]

hello,
i have a question about christoffel symbols . if we have :-
[PLAIN]http://www.tobikat.com
how can I derive these equations :-
[PLAIN]http://www.tobikat.com
please i want the answer be clear .


with very thanks...

You can have two different approaches in finding the components of geodesic equation, as arranged in the bottom picture. One is to calculate these all through tedious and lengthy geodesic equations or to simply take the path of Lagrange and utilize his equations to obtain what you want. But this latter one needs the line-element and since I don't see any (though I can guess what it could be), so you only seem to be left with the first method. So given those Christoffel symbols, just use the equations

[PLAIN]http://upload.wikimedia.org/math/d/f/9/df9964e9250e597ed0f1f23f3d1ddb21.png.[/URL]

Remember that here you must take the affine parameter $$\lambda$$ in place of t.

Ask where you feel stuck.

AB

 

[m.medhat]

thank you very much