diff options
| -rw-r--r-- | README | 8 | ||||
| -rw-r--r-- | journal/22jan2009.html | 5 | ||||
| -rw-r--r-- | journal/26jan2009.html | 27 | ||||
| -rw-r--r-- | other/doublepend-examples.scm | 81 | ||||
| -rw-r--r-- | other/henon-demos.scm | 15 | ||||
| -rw-r--r-- | work/calculus_play.scm | 17 |
6 files changed, 151 insertions, 2 deletions
@@ -32,3 +32,11 @@ journal/ daily journal entries proposal/ the original proposal as submited to the physics department +src/ + LaTeX, figures, source files, etc for actual document +work/ + Scheme code and examples +other/ + Misc other files +html/ + hypertext rendering of actual document diff --git a/journal/22jan2009.html b/journal/22jan2009.html index 68213b5..6ac454c 100644 --- a/journal/22jan2009.html +++ b/journal/22jan2009.html @@ -4,7 +4,7 @@ <head><title>bnewbold thesis</title></head> <body style="margin: 25px; font-family: helvetica;"> <h1 style="border-bottom: 2px solid;"> -Journal: Jan 21, 2009</h1> +Journal: Jan 22, 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> @@ -38,7 +38,8 @@ href="../other/mit-scheme-etch-amd64-howto.txt">directions</a> I emailed to the mit-scheme-devel list. <br /><br /> -<a href="21jan2009.html"><i>(previous entry)</i></a> +<a href="21jan2009.html"><i>(previous entry)</i></a> - +<a href="26jan2009.html"><i>(next entry)</i></a> <!-- ================================================================ --> <!-- ================================================================ --> diff --git a/journal/26jan2009.html b/journal/26jan2009.html new file mode 100644 index 0000000..2e7201e --- /dev/null +++ b/journal/26jan2009.html @@ -0,0 +1,27 @@ +<!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: Jan 26, 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 /> +<!-- ================================================================ --> +<!-- ================================================================ --> + +I need a running glossary of differential geometry terms as I read; it's +<a href="http://bnewbold.net/k/math/differentialgeometry/">here</a>. I'd like +to cross reference these against a couple textbooks and cherry pick the best +definitions/explinations. Early terms: coordinate function, chart, atlas, +patch, manifold, manifold function, vector field, coefficient function. + +<br /><br /> +<a href="22jan2009.html"><i>(previous entry)</i></a> + +<!-- ================================================================ --> +<!-- ================================================================ --> +</body> +</html> diff --git a/other/doublepend-examples.scm b/other/doublepend-examples.scm new file mode 100644 index 0000000..9f36ee0 --- /dev/null +++ b/other/doublepend-examples.scm @@ -0,0 +1,81 @@ +; from project 3 +; 8.351j +; bryan newbold + +; from section 1.6.2 + +(define ((T-pend m l g ys) local) + (let ((t (time local)) + (theta (coordinate local)) + (thetadot (velocity local))) + (let ((vys (D ys))) + (* 1/2 m + (+ (square (* 1 thetadot)) + (square (vys t)) + (* 2 l (vys t) thetadot (sin theta))))))) + +(define ((V-pend m l g ys) local) + (let ((t (time local)) + (theta (coordinate local))) + (* m g (- (ys t) (* l (cos theta)))))) + +(define L-pend (- T-pend V-pend)) + +(define ((periodic-drive amplitude frequency phase) t) + (* amplitude (cos (+ (* frequency t) phase)))) + +(define (L-periodically-driven-pendulum m l g a omega) + (let ((ys (periodic-drive a omega 0))) + (L-pend m l g ys))) + +(define Hamiltonian->state-derivative + phase-space-derivative) + +;(se ((Lagrangian->Hamiltonian +; (L-periodically-driven-pendulum 'm 'l 'g 'a 'omega)) +; (up 't 'theta 'p_theta))) + +(define (H-pend-sysder m l g a omega) + (Hamiltonian->state-derivative + (Lagrangian->Hamiltonian + (L-periodically-driven-pendulum m l g a omega)))) + +(define ((monitor-p-theta win) state) + (let ((q ((principal-value :pi) (coordinate state))) + (p (momentum state))) + (plot-point win q p))) + +(define window (frame :-pi :pi -100.0 100.0)) + +(let ((m 1.) + (l 9.8) + (g 9.8) + (A 0.01) + (omega 600)) + ((evolve H-pend-sysder m l g A omega) + (up 0. + 1.5367 + 0.) + (monitor-p-theta window) + .00001 + .6 + 1.0e-12)) + +(define (driven-pendulum-map m l g A omega) + (let ((advance (state-advancer H-pend-sysder m l g A omega)) + (map-period (/ :2pi omega))) + (lambda (theta ptheta return fail) + (let ((ns (advance + (up 0 theta ptheta) + map-period))) + (return ((principal-value :pi) (coordinate ns)) + (momentum ns)))))) + +(graphics-close window) +(start-gnuplot "output") + + + + + + diff --git a/other/henon-demos.scm b/other/henon-demos.scm new file mode 100644 index 0000000..c00e3fc --- /dev/null +++ b/other/henon-demos.scm @@ -0,0 +1,15 @@ +;;;;;;; problem 3.13 + +(define ((henon-map alpha) x y return failure) + (if (or (> x 1) (< x -1) (> y 1) (< y -1)) + failure) + (return (- (* x (cos alpha)) + (* (- y (square x)) (sin alpha))) + (+ (* x (sin alpha)) + (* (- y (square x)) (cos alpha))))) + +(define window (frame -1. 1. -1. 1.)) + +(explore-map window (henon-map 1.21) 2000) + + diff --git a/work/calculus_play.scm b/work/calculus_play.scm new file mode 100644 index 0000000..7a043df --- /dev/null +++ b/work/calculus_play.scm @@ -0,0 +1,17 @@ + +;;; Jan 26th + +(declare (usual-integrations)) +(load "~/thesis/scmutils/src/calculus/load.scm") + + +(define R2 (make-manifold R^n-type 2)) +(define U (patch 'origin R2)) + +(load "~/thesis/scmutils/src/general/canonicalizer.scm") + +(define d/dx (coordinate-basis-vector-field cart + +(define J (- (* x d/dy) (* y (d/dx)))) + +(define omega (literal-1form-field 'a R2-rect))
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