Christoffel symbols and geodesics, symbolic model

버전 1.3.0.0 (6.11 KB) 작성자: Ninetrees
Uses MATLAB symbolic processor to produce symbols
다운로드 수: 1K
업데이트 날짜: 2014/3/28

라이선스 보기

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.

인용 양식

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. 검색됨 .

MATLAB 릴리스 호환 정보
개발 환경: R2011a
모든 릴리스와 호환
플랫폼 호환성
Windows macOS Linux
카테고리
Help CenterMATLAB Answers에서 General Physics에 대해 자세히 알아보기

Community Treasure Hunt

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

Start Hunting!
버전 게시됨 릴리스 정보
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