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-rw-r--r--journal/02feb2009.html3
-rw-r--r--journal/04feb2009.html40
-rwxr-xr-xto_athena.sh2
-rw-r--r--work/funcdiff_play.scm93
4 files changed, 135 insertions, 3 deletions
diff --git a/journal/02feb2009.html b/journal/02feb2009.html
index 658538a..dea6f53 100644
--- a/journal/02feb2009.html
+++ b/journal/02feb2009.html
@@ -107,7 +107,8 @@ is not a coordinate basis." Isn't that just for orthogonal bases? Need to think
this through.
<br /><br />
-<a href="27jan2009.html"><i>(previous entry)</i></a>
+<a href="27jan2009.html"><i>(previous entry)</i></a> -
+<a href="04feb2009.html"><i>(next entry)</i></a>
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diff --git a/journal/04feb2009.html b/journal/04feb2009.html
new file mode 100644
index 0000000..d3d1cb1
--- /dev/null
+++ b/journal/04feb2009.html
@@ -0,0 +1,40 @@
+<!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: Feb 04, 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 />
+<!-- ================================================================ -->
+<!-- ================================================================ -->
+Started 8.962: General Relativity with Scott Hughes yesturday, I'm very
+enthusiastic. I'm surprised how large the class is, I'm greedily hoping it will
+thin out. My first impressions are that it will be very manageable given the
+background preparation I've done. We'll be doing "fundamentals" up through
+the spring break and applications after that, which fits my schedule well.
+
+<p />
+Yet another item on my reading queue is
+Laszlo Tisza's notes on Applied Geometric Algebra on
+<a href="http://ocw.mit.edu/ans7870/resources/tisza/index.htm">
+open courseware</a> from the 70's. I'm also poking through Lovelock and Rund's
+<u>Tensors, Differential Forms, and Variational Principles</u> as light
+background on tensor calculus as I work through the later parts of the
+differential geometry memo.
+
+<p />
+Other than that not much to report, first week of classes are leaving me enough
+time to keep reading but I haven't been playing/exploring on my own as much.
+Hopefully I'll get the chance to calculate some geodesics and come up with
+an outline on Friday.
+<br /><br />
+<a href="02jan2009.html"><i>(previous entry)</i></a>
+
+<!-- ================================================================ -->
+<!-- ================================================================ -->
+</body>
+</html>
diff --git a/to_athena.sh b/to_athena.sh
index 2de177d..f70d8b3 100755
--- a/to_athena.sh
+++ b/to_athena.sh
@@ -1,4 +1,4 @@
#!/bin/sh
#scp -r main.html journal other README bnewbold@linux.mit.edu:thesis/
-rsync -arv main.html journal other work src README bnewbold@linux.mit.edu:thesis/
+rsync -arv main.html journal work src README bnewbold@linux.mit.edu:thesis/
diff --git a/work/funcdiff_play.scm b/work/funcdiff_play.scm
index 482f0f3..f447253 100644
--- a/work/funcdiff_play.scm
+++ b/work/funcdiff_play.scm
@@ -300,4 +300,95 @@
; 0
; so [Jx,Jy] = -Jz, nice
-; @ p21? \ No newline at end of file
+;;; Feb 4
+
+(define setup-R2
+ (lambda ()
+ (let ()
+ (define R2 (rectangular 2))
+ (instantiate-coordinates R2 '(x y))
+ (define R2-point ((R2 '->point) (up 'x0 'y0))))))
+
+(define setup-R3
+ (lambda ()
+ (let ()
+ (define R3 (rectangular 3))
+ (instantiate-coordinates R3 '(x y z))
+ (define R3-point ((R3 '->point) (up 'x0 'y0 'z0))))))
+
+(setup-R2)
+
+(define v (+ (* 'a d/dx) (* 'b d/dy)))
+(define w (+ (* 'c d/dx) (* 'd d/dy)))
+
+;(pe (((wedge dx dy) v w) R2-point))
+
+(setup-R3)
+
+(define u (+ (* 'a d/dx) (* 'b d/dy) (* 'c d/dz)))
+(define v (+ (* 'd d/dx) (* 'e d/dy) (* 'f d/dz)))
+(define w (+ (* 'g d/dx) (* 'h d/dy) (* 'i d/dz)))
+
+;(pe (((wedge dx dy dz) u v w) R3-point))
+; determinant
+
+(define a (l-m-f 'alpha R3))
+(define b (l-m-f 'beta R3))
+(define c (l-m-f 'gamma R3))
+
+(define theta (+ (* a dx) (* b dy) (* c dz)))
+
+(define X (literal-vector-field 'X R3))
+(define Y (literal-vector-field 'Y R3))
+
+#|
+(pe (((- (d theta)
+ (+ (wedge (d a) dx)
+ (wedge (d b) dy)
+ (wedge (d c) dz)))
+ X Y)
+ R3-point))
+;0
+
+|#
+
+(define ((vector-field-over-map mu:N->M) v-on-M)
+ (procedure->vector-field
+ (lambda (f-on-M)
+ (compose (v-on-M f-on-M) mu:N->M))))
+
+(define (vector-field-over-map->vector-field V-over-mu n)
+ (procedure->vector-field
+ (lambda (f)
+ (lambda (m) ((V-over-mu f) n)))))
+
+(define ((form-field-over-map mu:N->M) w-on-M)
+ (let ((k (get-rank w-on-M)))
+ (procedure->nform-field
+ (lambda vecotrs-over-map
+ (lambda (n)
+ ((apply w-on-M
+ (map (lambda (V-over-mu)
+ (vector-field-over-map->vector-field
+ V-over-mu n))
+ vectors-over-map))
+ (mu:N->M n))))
+ 'athing
+ k)))
+
+(pp procedure->nform-field)
+
+(define sphere (S2 1))
+(instantiate-coordinates sphere '(theta phi))
+(define sphere-basis (coordinate-system->basis sphere))
+(instantiate-coordinates the-real-line 't)
+
+(define mu
+ (compose (sphere '->point)
+ (up (literal-function 'alpha)
+ (literal-function 'beta))
+ (the-real-line '->coords)))
+
+(define sphere-basis-over-mu
+ (basis->basis-over-map mu sphere-basis))
+