From b006651e7a270f81f4071a36b91e1a924219bdfc Mon Sep 17 00:00:00 2001 From: bnewbold Date: Sat, 20 Jun 2009 03:58:43 -0400 Subject: last clean up --- journal/31mar2009.html | 84 ++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 84 insertions(+) create mode 100644 journal/31mar2009.html (limited to 'journal/31mar2009.html') diff --git a/journal/31mar2009.html b/journal/31mar2009.html new file mode 100644 index 0000000..bbf2e3b --- /dev/null +++ b/journal/31mar2009.html @@ -0,0 +1,84 @@ + + +bnewbold thesis + +

+Journal: March 31, 2009

+Bryan Newbold, bnewbold@mit.edu
+ +http://web.mit.edu/bnewbold/thesis/ +

+ + + +Some more papers from trolling around the net, some are great! +

Algorithms for computer algebra calculations in spacetime: + I. The calculation of curvature by D. Pollney et al, 1996, + Class. Quantum Grav.
+Haven't read through this yet but looks nice, compares other packages and +presents algorithms. I don't know what any subsequent articles were... + +
Computer Algebra Systems in General Relativity + Salah Haggag, (Conference Paper) 2007
+Just a review, some good history and excellent bibliography. + +
Numerical Experimentation within GRworkbench + Andrew Moylan, Undergrad Thesis at ANU, 2003. + Also GRworkbench: A Computational System Based on Differential + Geometry and Functional Programming Framework for GRworkbench. +
+Wow! Great stuff, too bad I can't find the software actually hosted anywhere +(links are all dead). Written in C++ with templates for common calculations, +GUI interface, functional (combinator-based) scripting language hacked on, etc. +The intro paper is really clearly written from a CS standpoint, explicitly +lists all the geometric concepts and the software equivalents. +

+ +

+ +Last night I started working through the anomalous precession calculation +(see anomalous_precession.scm). +I generated a new coordinate system for the 2+1 polar spacetime with a +Schwartzchild metric and was able to derive the Christofel symbols (though +in a frustratingly "simplified" form): + +

+(down
+ (down (up 0 (+ (/ (* -2 (expt M 2)) (expt r0 3)) (/ M (expt r0 2))) 0)
+       (up (/ (* -1/2 M) (+ (* M r0) (* -1/2 (expt r0 2)))) 0 0)
+       (up 0 0 0))
+ (down (up (/ (* -1/2 M) (+ (* M r0) (* -1/2 (expt r0 2)))) 0 0)
+       (up 0 (/ (* 1/2 M) (+ (* M r0) (* -1/2 (expt r0 2)))) 0)
+       (up 0 0 (/ 1 r0)))
+ (down (up 0 0 0) (up 0 0 (/ 1 r0)) (up 0 (+ (* 2 M) (* -1 r0)) 0)))
+

+ +

+I got stuck when I tried to take a covariant derivative of a dummy test path +to derive the geodesic equations of motion; there are a lot of dt dummy +variables floating around so I installed new coordinates for the-real-line to +use 'k' instead of 't'; but I still get: +

+(((((covariant-derivative polar-Cartan-over-path) d/dk)
+   ((differential test-path) d/dk))
+  (orbital-plane-polar '->coords))
+ ((the-real-line '->point) 'k))
+
+;Bad selectors -- DERIV:EUCLIDEAN-STRUCTURE #[compiled-closure 13 (lambda "mathutil" #x1b) #xed0 #xbbbb4c #x1fdb064] (0) k
+

+Fiddling about with this expression frequently results in an assertion error +when the orbital-plane-polar coordinate system is passed a the-real-line point. +

+I should go through and derive some more pedestrian geodesics and sure i'm doing +things right. +

+ +(previous entry) + + + + + -- cgit v1.2.3