diff --git a/physics-compiler.lisp b/physics-compiler.lisp
index 0de5f60..3e019ec 100644
--- a/physics-compiler.lisp
+++ b/physics-compiler.lisp
@@ -38,12 +38,6 @@
 	 ,(enmaxima-lagrangian lagrangian)
 	 ,(enmaxima-coords coords))))
 
-(defun momentum-symbol (q)
-  (intern (format nil "P_~a" (symbol-name q))))
-
-(defun flatten (l)
-  (apply #'append l))
-
 (defun unmaxima-expression (expr)
   (defun unmaxima-symbol (sym)
 	(let ((name (symbol-name sym)))
@@ -56,17 +50,24 @@
 	((listp expr) (mapcar #'unmaxima-expression expr))
 	(t expr)))
 
+(defun momentum-symbol (q)
+  (intern (format nil "P_~a" (symbol-name q))))
+
+(defun next-symbol (s)
+  (intern (format nil "NEXT-~a" (symbol-name s))))
+
 (defun update-logic (result coords)
-  (defun coord-updates (exprs q)
-	(let ((p (momentum-symbol q))
-		  (q-dot-expr (cadr exprs))
-		  (p-dot-expr (caddr exprs)))
-	  `((incf ,p (* dt ,(unmaxima-expression p-dot-expr)))
-		(incf ,q (* dt ,(unmaxima-expression q-dot-expr))))))
-  (flatten (loop for coord-expressions
-				   in (cdr (maxima-interface::maxima-to-lisp result))
-				 for q in coords
-				 collect (coord-updates coord-expressions q))))
+  (defun coord-update (q exprs)
+	`(,(next-symbol q)
+	  (+ ,q (* dt ,(unmaxima-expression (cadr exprs))))))
+  (defun momentum-update (q exprs)
+	(let ((p (momentum-symbol q)))
+	  `(,(next-symbol p)
+		(+ ,p (* dt ,(unmaxima-expression (caddr exprs)))))))
+  (loop for exprs in (cdr (maxima-interface::maxima-to-lisp result))
+        for q in coords
+		collect (coord-update q exprs)
+		collect (momentum-update q exprs)))
 
 (defun keys (plist)
   (loop for key in plist by #'cddr collect key))
@@ -75,7 +76,7 @@
   (let ((vars (append coords (mapcar #'momentum-symbol coords))))
     `(let (,@(mapcar (lambda (s) `(,s (getf params ',s))) (keys params))
            ,@(mapcar (lambda (s) `(,s (getf state ',s))) vars))
-	   ,@(update-logic result coords)
-	   (list ,@(flatten
-				(mapcar (lambda (s) (list `',s s))
-						vars))))))
+	   (let ,(update-logic result coords)
+		 (list ,@(loop for s in vars
+					   collect `',s
+					   collect (next-symbol s)))))))