Christoffel symbols and geodesics, symbolic model

Version 1.3.0.0 (6,11 KB) von Ninetrees
Uses MATLAB symbolic processor to produce symbols
1,1K Downloads
Aktualisiert 28. Mär 2014

Lizenz anzeigen

This is a MATLAB document to symbolically compute Christoffel symbols and geodesic equations, using a given metric gαβ. Justification for the method is found in various texts on general relativity, and is not duplicated here. By working through Lagrange's equations for the line element of a given metric, such as the wormhole metric,
ds^2 = -dt^2 +dr^2 + (b^2 + r^2) * (dΘ^2 + sin^2 (Θ) dΦ^2)
a general expression for the Christoffel symbols of the metric and its derivatives is obtained. Though this illustrates the use of MATLAB, it is more educational than functional. Nonetheless, Gamma /is/ the MDA of Christoffel symbols for this metric, and the geodesic, however plainly displayed, is complete.
This script contains comments for those coming to MATLAB from other platforms.
I posted a Mathcad version of this on the PTC forum (web search), along with the MATLAB code (by request). My purpose is to make the material available to a wider audience.

Zitieren als

Ninetrees (2024). Christoffel symbols and geodesics, symbolic model (https://www.mathworks.com/matlabcentral/fileexchange/45901-christoffel-symbols-and-geodesics-symbolic-model), MATLAB Central File Exchange. Abgerufen .

Kompatibilität der MATLAB-Version
Erstellt mit R2011a
Kompatibel mit allen Versionen
Plattform-Kompatibilität
Windows macOS Linux
Kategorien
Mehr zu General Physics finden Sie in Help Center und MATLAB Answers

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Version Veröffentlicht Versionshinweise
1.3.0.0

Updated to include Symbolic Math Toolbox

1.2.0.0

Included reference to Mathcad equivalent file.

1.1.0.0

Edited description for display, not for content.

1.0.0.0