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pendulum.clj
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pendulum.clj
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;
; Copyright © 2017 Colin Smith.
; This work is based on the Scmutils system of MIT/GNU Scheme:
; Copyright © 2002 Massachusetts Institute of Technology
;
; This is free software; you can redistribute it and/or modify
; it under the terms of the GNU General Public License as published by
; the Free Software Foundation; either version 3 of the License, or (at
; your option) any later version.
;
; This software is distributed in the hope that it will be useful, but
; WITHOUT ANY WARRANTY; without even the implied warranty of
; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
; General Public License for more details.
;
; You should have received a copy of the GNU General Public License
; along with this code; if not, see <http://www.gnu.org/licenses/>.
;
;; The simple pendulum supported at the point x (in the plane; x should
;; be a function of t returning an up-tuple (up xt yt).
(ns sicmutils.examples.pendulum
(:refer-clojure :exclude [+ - * / zero? partial ref])
(:require [sicmutils.env :refer :all]))
(defn T
[m l _ x]
(let [v (D x)]
(fn [[t θ θdot]]
(let [[vx vy :as vt] (v t)]
(* 1/2 m
(+ (square vt)
(* 2 l θdot (+ (* vy (sin θ)) (* vx (cos θ))))
(square (* l θdot))))))))
(defn V
[m l g x]
(fn [[t θ _]]
(* m g (- (ref (x t) 1) (* l (cos θ))))))
(def L (- T V))