Christoffelsymbole - Versionsgeschichte

Schubotz am 16. September 2010 um 21:02 Uhr

2010-09-16T21:02:28Z

← Nächstältere Version		Version vom 16. September 2010, 23:02 Uhr
Zeile 18:		Zeile 18:

	:<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>		:<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]]

*>SchuBot: Mathematik einrücken

2010-09-12T16:09:15Z

Mathematik einrücken

← Nächstältere Version		Version vom 12. September 2010, 18:09 Uhr
Zeile 11:		Zeile 11:
	</math>		</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>		:<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>


Zeile 17:		Zeile 17:


	<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>		:<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>

85.179.11.30 am 10. April 2009 um 11:13 Uhr

2009-04-10T11:13:25Z

← Nächstältere Version		Version vom 10. April 2009, 13:13 Uhr
Zeile 6:		Zeile 6:
	{{g}_{\sigma {\color{Violet}\mu } ,{\color{Red}\nu} }}		{{g}_{\sigma {\color{Violet}\mu } ,{\color{Red}\nu} }}
	+		+
	{{g}_{\sigma {\color{Red}\nu} ,{\color{~~Brown~~}\mu } }}		{{g}_{\sigma {\color{Red}\nu} ,{\color{Violet}\mu } }}
	-		-
	{{g}_{{\color{Red}\mu} {\color{Violet}\nu } ,\sigma }} \right)		{{g}_{{\color{Red}\mu} {\color{Violet}\nu } ,\sigma }} \right)
	</math>		</math>

	<math>\Gamma _{\mu \nu }^{\alpha }=\frac{\color{~~Violet~~}\partial {{x}^{\alpha }}}{\partial {{\xi }^{\beta }}}\frac{{{\partial }^{2}}{{\xi }^{\beta }}}{\partial {{x}^{\mu }}\partial {{x}^{\nu }}}</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>


Zeile 17:		Zeile 17:


	<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{\partial x{{'}^{\alpha }}}{\partial {{x}^{\beta }}}\frac{{{\partial }^{2}}{{x}^{\beta }}}{\partial x{{'}^{\mu }}\partial x{{'}^{\nu }}}</math>		<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>

85.179.11.30 am 10. April 2009 um 11:11 Uhr

2009-04-10T11:11:57Z

← Nächstältere Version		Version vom 10. April 2009, 13:11 Uhr
Zeile 6:		Zeile 6:
	{{g}_{\sigma {\color{Violet}\mu } ,{\color{Red}\nu} }}		{{g}_{\sigma {\color{Violet}\mu } ,{\color{Red}\nu} }}
	+		+
	{{g}_{\sigma {\color{Red}\nu} ,{\color{~~Violet~~}\mu } }}		{{g}_{\sigma {\color{Red}\nu} ,{\color{Brown}\mu } }}
	-		-
	{{g}_{{\color{Red}\mu} {\color{Violet}\nu } ,\sigma }} \right)		{{g}_{{\color{Red}\mu} {\color{Violet}\nu } ,\sigma }} \right)
	</math>		</math>

			<math>\Gamma _{\mu \nu }^{\alpha }=\frac{\color{Violet}\partial {{x}^{\alpha }}}{\partial {{\xi }^{\beta }}}\frac{{{\partial }^{2}}{{\xi }^{\beta }}}{\partial {{x}^{\mu }}\partial {{x}^{\nu }}}</math>


	== Verhalten bei Koordinatentransformation ==		== 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{\partial x{{'}^{\alpha }}}{\partial {{x}^{\beta }}}\frac{{{\partial }^{2}}{{x}^{\beta }}}{\partial x{{'}^{\mu }}\partial x{{'}^{\nu }}}</math>

85.179.11.30 am 10. April 2009 um 10:56 Uhr

2009-04-10T10:56:50Z

← Nächstältere Version		Version vom 10. April 2009, 12:56 Uhr
Zeile 1:		Zeile 1:
	<math>		<math>
	\Gamma _{{\color{Red}\nu} {\color{Violet}\~~rho~~ } }^{{\color{Orange}\mu}}		\Gamma _{{\color{Red}\mu} {\color{Violet}\nu } }^{{\color{Orange}\alpha}}
	=		=
	\frac{1}{2}		\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>


	== Verhalten bei Koordinatentransformation ==		== Verhalten bei Koordinatentransformation ==

Schubotz am 3. April 2009 um 12:35 Uhr

2009-04-03T12:35:11Z

← Nächstältere Version		Version vom 3. April 2009, 14:35 Uhr
Zeile 10:		Zeile 10:
	{{g}_{{\color{Red}\nu} {\color{Violet}\rho } ,\alpha }} \right)		{{g}_{{\color{Red}\nu} {\color{Violet}\rho } ,\alpha }} \right)
	</math>		</math>

			== Verhalten bei Koordinatentransformation ==

Schubotz am 2. April 2009 um 08:51 Uhr

2009-04-02T08:51:20Z

← Nächstältere Version		Version vom 2. April 2009, 10:51 Uhr
Zeile 1:		Zeile 1:
	<math>\Gamma _{\nu \rho }^\mu = \frac{1}{2}{g^{\mu \alpha }}\left( {{\~~partial _~~\rho }{g_{~~\alpha~~ \nu }} + {\~~partial _~~\nu }{g_{~~\alpha~~ \rho }} - {\~~partial _~~\~~alpha~~ }{g_{~~\nu~~ \rho }}} \right)</math>		<math>
			\Gamma _{{\color{Red}\nu} {\color{Violet}\rho } }^{{\color{Orange}\mu}}
			=
			\frac{1}{2}
			{{g}^{{\color{Orange}\mu}\alpha }}\left(
			{{g}_{\alpha {\color{Violet}\rho } ,{\color{Red}\nu} }}
			+
			{{g}_{\alpha {\color{Red}\nu} ,{\color{Violet}\rho } }}
			-
			{{g}_{{\color{Red}\nu} {\color{Violet}\rho } ,\alpha }} \right)
			</math>

Schubotz: Die Seite wurde neu angelegt: $\Gamma _{\nu \rho }^\mu = \frac{1}{2}{g^{\mu \alpha }}\left( {{\partial _\rho }{g_{\alpha \nu }} + {\partial _\nu }{g_{\alpha \rho }} - {\partial _\alpha }{g_{\n...$

2009-03-19T12:45:35Z

Die Seite wurde neu angelegt: <math>\Gamma _{\nu \rho }^\mu = \frac{1}{2}{g^{\mu \alpha }}\left( {{\partial _\rho }{g_{\alpha \nu }} + {\partial _\nu }{g_{\alpha \rho }} - {\partial _\alpha }{g_{\n...

Neue Seite

<math>\Gamma _{\nu \rho }^\mu = \frac{1}{2}{g^{\mu \alpha }}\left( {{\partial _\rho }{g_{\alpha \nu }} + {\partial _\nu }{g_{\alpha \rho }} - {\partial _\alpha }{g_{\nu \rho }}} \right)</math>