particle-mzscheme.ss

(define (naive-euler w)
 (let* ((charges (list (list 10.0 (d- 10.0 w)) (list 10.0 0.0)))
	(x-initial (list 0.0 8.0))
	(xdot-initial (list 0.75 0.0))
	(delta-t 1e-1)
	(p (lambda (x)
	    ((reduce d+ 0.0)
	     (map (lambda (c) (d/ 1.0 (distance x c))) charges)))))
  (letrec ((loop
	    (lambda (x xdot)
	     (let* ((xddot (k*v -1.0 ((gradient p) x)))
		    (x-new (v+ x (k*v delta-t xdot))))
	      (if (dpositive? (list-ref x-new 1))
		  (loop x-new (v+ xdot (k*v delta-t xddot)))
		  (let* ((delta-t-f (d/ (d- 0.0 (list-ref x 1))
					(list-ref xdot 1)))
			 (x-t-f (v+ x (k*v delta-t-f xdot))))
		   (sqr (list-ref x-t-f 0))))))))
   (loop x-initial xdot-initial))))

(define (particle)
 (my-write (let* ((w0 0.0)
		  (w*-list
		   (multivariate-argmin
		    (lambda (w-list) (naive-euler (car w-list))) (list w0))))
	    (car w*-list))))