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| author | bnewbold <bnewbold@eta.mit.edu> | 2009-06-20 03:58:43 -0400 |
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| committer | bnewbold <bnewbold@eta.mit.edu> | 2009-06-20 03:58:43 -0400 |
| commit | b006651e7a270f81f4071a36b91e1a924219bdfc (patch) | |
| tree | 585c843d21eb78a2a8572fda5cfadc347449c524 /journal/31mar2009.html | |
| parent | ac2109a577a0ddaddf0ddf5d99b91616f4b72546 (diff) | |
| download | 8thesis-b006651e7a270f81f4071a36b91e1a924219bdfc.tar.gz 8thesis-b006651e7a270f81f4071a36b91e1a924219bdfc.zip | |
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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 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" +"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> +<html xmlns="http://www.w3.org/1999/xhtml"> +<head><title>bnewbold thesis</title></head> +<body style="margin: 25px; font-family: helvetica;"> +<h1 style="border-bottom: 2px solid;"> +Journal: March 31, 2009</h1> +<i>Bryan Newbold, <a href="mailto:bnewbold@mit.edu">bnewbold@mit.edu</a></i><br /> +<i><a href="http://web.mit.edu/bnewbold/thesis/"> +http://web.mit.edu/bnewbold/thesis/</a></i> +<br /><p /> +<!-- ================================================================ --> +<!-- ================================================================ --> + +Some more papers from trolling around the net, some are great! +<ul> + <li /><b>Algorithms for computer algebra calculations in spacetime: + I. The calculation of curvature</b> by D. Pollney et al, 1996, + Class. Quantum Grav.<br /> +Haven't read through this yet but looks nice, compares other packages and +presents algorithms. I don't know what any subsequent articles were... + + <li /><b>Computer Algebra Systems in General Relativity</b> + Salah Haggag, (Conference Paper) 2007<br /> +Just a review, some good history and excellent bibliography. + + <li /><b>Numerical Experimentation within GRworkbench</b> + Andrew Moylan, Undergrad Thesis at ANU, 2003. + Also <b>GRworkbench: A Computational System Based on Differential + Geometry</b> and <b>Functional Programming Framework for GRworkbench</b>. + <br /> +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. +</ul> + +<hr /> + +Last night I started working through the anomalous precession calculation +(see <a href="../work/anomalous_precession.scm">anomalous_precession.scm</a>). +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): + +<pre style="margin:20px; border-left: solid grey 3px; background-color:lightgrey;padding:5px;width:750px;"> +(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))) +</pre> + +<p /> +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: +<pre style="margin:20px; border-left: solid grey 3px; background-color:lightgrey;padding:5px;width:750px;"> +(((((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 +</pre> +<p /> +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. +<p /> +I should go through and derive some more pedestrian geodesics and sure i'm doing +things right. +<br /><br /> + +<a href="15apr2009.html"><i>(previous entry)</i></a> + +<!-- ================================================================ --> +<!-- ================================================================ --> +</body> +</html> |