t686 Posted September 1, 2019 Share Posted September 1, 2019 (edited) test Edited September 1, 2019 by t686 Link to comment Share on other sites More sharing options...

Orion1 Posted October 25, 2020 Share Posted October 25, 2020 this is a test. Link to comment Share on other sites More sharing options...

studiot Posted October 26, 2020 Share Posted October 26, 2020 (edited) [math]\begin{array} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\\end{array}[/math] Edited October 26, 2020 by studiot Link to comment Share on other sites More sharing options...

studiot Posted October 26, 2020 Share Posted October 26, 2020 (edited) 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 Link to comment Share on other sites More sharing options...

Col Not Colin Posted February 5 Share Posted February 5 (edited) [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 by Col Not Colin Link to comment Share on other sites More sharing options...

Col Not Colin Posted February 5 Share Posted February 5 (edited) 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 by Col Not Colin Link to comment Share on other sites More sharing options...

studiot Posted March 11 Share Posted March 11 [math]\begin{array}{*{20}{c}} {62310721} \\ {\underline {25644387} } \\ {87955108} \\ \end{array}[/math] [math]\begin{array}{l} 62310721 \\ \underline {00000007} \\ 62310728 \\ \end{array}[/math] Link to comment Share on other sites More sharing options...

## Recommended Posts

## Create an account or sign in to comment

You need to be a member in order to leave a comment

## Create an account

Sign up for a new account in our community. It's easy!

Register a new account## Sign in

Already have an account? Sign in here.

Sign In Now