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| -rw-r--r-- | journal/02feb2009.html | 3 | ||||
| -rw-r--r-- | journal/04feb2009.html | 40 | ||||
| -rwxr-xr-x | to_athena.sh | 2 | ||||
| -rw-r--r-- | work/funcdiff_play.scm | 93 |
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> <!-- ================================================================ --> <!-- ================================================================ --> 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)) + |