sicmutils

(nextjournal.env/load! :sicmutils)

(+ (square (sin 'x))

    (square (cos 'y)))

(literal-function 'U)

(defn L-central-polar [m U]

  (fn [[_ [r] [rdot φdot]]]

    (- (* 1/2 m

         (+ (square rdot)

           (square (* r φdot))))

      (U r))))

(let [potential-fn (literal-function 'U)

      L (L-central-polar 'm potential-fn)

      state (up (literal-function 'r)

              (literal-function 'φ))]

  (((Lagrange-equations L) state) 't))