(define (Lagrange-eq L q)
  (- (D (compose ((partial 2) L) (Gamma q)))
     (compose ((partial 1) L) (Gamma q))))

(define (V x y)
  (+ (/ (+ (square x) (square y)) 2)
     (* (square x) y)
     (- (/ (cube y) 3))))

(define ((L m) local)
  (let ((vx (ref (velocity local) 0))
        (vy (ref (velocity local) 1))
        ( x (ref (coordinate local) 0))
        ( y (ref (coordinate local) 1)))
    (- (/ (* m (+ (square vx) (square vy))) 2)
       (V x y))))

(define (q t)
  (up
   ((literal-function 'x) t)
   ((literal-function 'y) t)))

(print-expression
  ((Lagrange-eq (L 'm) q) 't))
)