Christoffelsymbole: Unterschied zwischen den Versionen

Aktuelle Version vom 16. September 2010, 23:02 Uhr

Γ_{μ ν}^{α} = \frac{\partial x^{α}}{\partial ξ^{β}} \frac{\partial^{2} ξ^{β}}{\partial x^{μ} \partial x^{ν}}

Γ'_{μ ν}^{α} = \frac{\partial x'^{α}}{\partial x^{β}} \frac{\partial x^{ρ}}{\partial x'^{μ}} \frac{\partial x^{σ}}{\partial x'^{ν}} Γ_{ρ σ}^{β} + \frac{\partial x'^{α}}{\partial x^{β}} \frac{\partial^{2} x^{β}}{\partial x'^{μ} \partial x'^{ν}}

@@ Zeile 1: / Zeile 1: @@
 <math>
-\Gamma _{{\color{Red}\nu} {\color{Violet}\rho } }^{{\color{Orange}\mu}}
+\Gamma _{{\color{Red}\mu} {\color{Violet}\nu } }^{{\color{Orange}\alpha}}
 =
 \frac{1}{2}
-{{g}^{{\color{Orange}\mu}\alpha }}\left(
+{{g}^{{\color{Orange}\alpha}\sigma }}\left(
-{{g}_{\alpha {\color{Violet}\rho } ,{\color{Red}\nu} }}
+{{g}_{\sigma {\color{Violet}\mu } ,{\color{Red}\nu} }}
 +
-{{g}_{\alpha {\color{Red}\nu} ,{\color{Violet}\rho } }}
+{{g}_{\sigma {\color{Red}\nu} ,{\color{Violet}\mu } }}
 -
-{{g}_{{\color{Red}\nu} {\color{Violet}\rho } ,\alpha }} \right)
+{{g}_{{\color{Red}\mu} {\color{Violet}\nu } ,\sigma }} \right)
 </math>
+:<math>\Gamma _{\mu \nu }^{\alpha }=\frac{\color{Brown}\partial {{x}^{\alpha }}}{\partial {{\xi }^{\beta }}}\frac{{{\partial }^{2}}{{\xi }^{\beta }}}{\color{Brown}\partial {{x}^{\mu }}\partial {{x}^{\nu }}}</math>
 == Verhalten bei Koordinatentransformation ==
+:<math>\Gamma{'}_{\mu \nu }^{\alpha }=\frac{\partial x{{'}^{\alpha }}}{\partial {{x}^{\beta }}}\frac{\partial {{x}^{\rho }}}{\partial x{{'}^{\mu }}}\frac{\partial {{x}^{\sigma }}}{\partial x{{'}^{\nu }}}\Gamma _{\rho \sigma }^{\beta }+\frac{\color{Brown}\partial x{{'}^{\alpha }}}{\partial {{x}^{\beta }}}\frac{{{\partial }^{2}}{{x}^{\beta }}}{\color{Brown}\partial x{{'}^{\mu }}\partial x{{'}^{\nu }}}</math>
+[[Kategorie:ART]]