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t686
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  • 1 year later...

I can see my table in the list in the activity tab, but I can't see it in the thread itself.

This is even after refreshing the thread in the normal manner for MathML.

[math]\begin{array}{*{20}{c}}

    +  & 0 & 1  \\

   0 & 0 & 1  \\

   1 & 1 & 1  \\

\end{array}[/math]

 

 

[math]\left( {\begin{array}{*{20}{c}}

    +  & 0 & 1  \\

   0 & 0 & 1  \\

   1 & 1 & 1  \\

\end{array}} \right)[/math]

[math]\begin{array}

    +  & 0 & 1  \\

   0 & 0 & 1  \\

   1 & 1 & 1  \\

\end{array}[/math]

 

 

[math]\left( {\begin{array}

    +  & 0 & 1  \\

   0 & 0 & 1  \\

   1 & 1 & 1  \\

\end{array}} \right)[/math]

Edited by studiot
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  • 3 months later...

[math] \frac {d^2 x^{\mu}} {d \alpha^2} + \Gamma_{\rho \sigma}^{\mu} \frac {dx^{\rho} } {d \alpha }  \frac {dx^{\sigma}} {d \alpha} [/math]

 

Same again, in larger font:

[math] \frac {d^2 x^{\mu}} {d \alpha^2} + \Gamma_{\rho \sigma}^{\mu} \frac {dx^{\rho} } {d \alpha }  \frac {dx^{\sigma}} {d \alpha} [/math]

Test post:

The following is the usual geodesic equation from General Relativity:

[math] \frac {d^2 x^{\mu}} {d \tau^2} + \Gamma_{\rho \sigma}^{\mu} \frac {dx^{\rho} } {d \tau }  \frac {dx^{\sigma}} {d \tau} [/math]

Where [math] \tau [/math] is an affine parameter (for example, proper time)  and the path is given by  [math] x^\mu = x^\mu  (\tau) [/math]

Suppose the same path is parameterised another way.  Let  [math] x^\mu = x^\mu (\lambda) [/math] where the parameter [math] \lambda [/math]  is NOT assumed to be an affine parameter.  

Then,  [math] \frac {d x^\mu} {d \lambda} = \frac {d x^\mu} {d \tau}  . \frac {d \tau} {d \lambda}  [/math]   by the chain rule and since we can assume [math] \frac {d \tau} {d \lambda}  [/math] exists without loss of generality.

 

 

 

 

 

Edited by Col Not Colin
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Latex test:

[math] \frac {d^2 x^{\mu}} {d \alpha^2} + \Gamma_{\rho \sigma}^{\mu} \frac {dx^{\rho} } {d \alpha }  \frac {dx^{\sigma}} {d \alpha} [/math]

 

Same again, in larger font:

[math] \frac {d^2 x^{\mu}} {d \alpha^2} + \Gamma_{\rho \sigma}^{\mu} \frac {dx^{\rho} } {d \alpha }  \frac {dx^{\sigma}} {d \alpha} [/math]

Test post:

The following is the usual geodesic equation from General Relativity:

[Eqn 1]          [math] \frac {d^2 x^{\mu}} {d \tau^2} + \Gamma_{\rho \sigma}^{\mu} \frac {dx^{\rho} } {d \tau }  \frac {dx^{\sigma}} {d \tau} = 0 [/math]

Where [math] \tau [/math] is an affine parameter (for example, proper time)  and the path is given by  [math] x^\mu = x^\mu  (\tau) [/math]

Suppose the same path is parameterised another way.  Let  [math] x^\mu = x^\mu (\lambda) [/math] where the parameter [math] \lambda [/math]  is NOT assumed to be an affine parameter.  

Then, 

[Eqn 2]     [math] \frac {d x^\mu} {d \lambda} = \frac {d x^\mu} {d \tau}   \frac {d \tau} {d \lambda}  [/math]   by the chain rule (we can assume [math] \frac {d \tau} {d \lambda}  [/math] exists).

Hence,

[Eqn 3]     [math] \frac {d^2 x^\mu} {d \lambda ^2} = \frac {d^2 x^\mu} {d \tau ^2}  {\frac {d \tau} {d \lambda}}^2  +  \frac {d x^\mu} {d \tau}   \frac {d^2 \tau} {d \lambda ^2}  [/math]

Combining Eqn 1 and Eqn 2 we obtain,

[math] \frac {d^2 x^{\mu}} {d \lambda^2} +  \Gamma_{\rho \sigma}^{\mu} \frac {dx^{\rho} } {d \lambda }  \frac {dx^{\sigma}} {d \lambda}  \space = \space \frac {d x^{\mu}} {d \tau} \frac {d^2 \tau} {d \lambda ^2} +  \large [ \normalsize {\frac {d \tau} {d \lambda}} \large ] \normalsize ^2 \large ( \normalsize \frac {d^2 x^{\mu}} {d \tau^2} + \Gamma_{\rho \sigma}^{\mu} \frac {dx^{\rho} } {d \tau }  \frac {dx^{\sigma}} {d \tau} \large ) [/math]

COMMENT:  having a time-limit to edit posts in the sandbox seems un-kind.  Sorry for making a lot of posts, I ran out of time.  Crumbs... this is hard work.  I'll try an equation editor and see if I can import the finished thing.

Edited by Col Not Colin
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  • 1 month later...


[math]\begin{array}{*{20}{c}}
   {62310721}  \\
   {\underline {25644387} }  \\
   {87955108}  \\
\end{array}[/math]

 


[math]\begin{array}{l}
 62310721 \\
 \underline {00000007}  \\
 62310728 \\
 \end{array}[/math]

 

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