test

[t686]

test

Edited September 1, 2019 by t686

[Orion1]

this is a test.

[studiot]

[math]\begin{array}  +  & 0 & 1  \\ 0 & 0 & 1  \\ 1 & 1 & 1  \\\end{array}[/math]

Edited October 26, 2020 by studiot

[studiot]

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 October 26, 2020 by studiot

[Col Not Colin]

[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 February 5, 2021 by Col Not Colin

[Col Not Colin]

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 February 5, 2021 by Col Not Colin

[studiot]

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

 

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

 

[joigus]

17 minutes ago, Gary_McGrath said:

What is the point of this topic?

Quote

The Sandbox

This forum is provided for members to test BB code, learn how to use the various forum functions, and generally get to grips with the system. All options are turned on, but posts do not count towards your total.

 

[iNow]

3 hours ago, Gary_McGrath said:

What is the point of this topic?

To test stuff. It's right there in the title.