Noether Theorem Support

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(ns emmy.mechanics.noether

  (:refer-clojure :exclude [partial])

  (:require [emmy.calculus.derivative :refer [D partial]]

            [emmy.function :as f]

            [emmy.generic :as g]))

Noether Theorem Support

F-tilde is a parametric coordinate transformation that given parameters takes a state and returns transformed coordinates. F-tilde may take an arbitrary number of real-valued parameters. F-tilde applied to zeros is the coordinate selector: It takes a state and returns the coordinates. The hypothesis of Noether's theorem is that the Lagrangian is invariant under the transformation for all values of the parameters.

(D (lambda parms (compose L (F->C (apply F-tilde parms))))) = 0

(defn Noether-integral [L F-tilde]

  (let [min-arity (second (f/arity F-tilde))

        zeros     (repeat min-arity 0)]

    (g/* ((partial 2) L) (apply (D F-tilde) zeros))))

#object[emmy.mechanics.noether$Noether_integral 0x4a36207d "

emmy.mechanics.noether$Noether_integral@4a36207d"

]