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authorbnewbold <bnewbold@eta.mit.edu>2009-06-20 03:58:43 -0400
committerbnewbold <bnewbold@eta.mit.edu>2009-06-20 03:58:43 -0400
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+<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 '-&gt;coords))
+ ((the-real-line '-&gt;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>