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2 | 2 | :clay {:title "Emmy, the Algebra System: Classical Mechanics Prologue" |
3 | 3 | :quarto {:author :kloimhardt |
4 | 4 | :type :post |
5 | | - :date "2025-09-10" |
6 | | - :image "sicm_ch01.png" |
| 5 | + :date "2025-11-12" |
| 6 | + :image "fdg_prologue.png" |
7 | 7 | :category :libs |
8 | 8 | :tags [:emmy :physics]}}} |
9 | | -(ns mentat-collective.emmy.fdg-ch01 |
| 9 | +(ns mentat-collective.emmy.fdg-prologue |
10 | 10 | (:require [scicloj.kindly.v4.api :as kindly] |
11 | 11 | [scicloj.kindly.v4.kind :as kind] |
12 | | - [emmy.env :as e] |
| 12 | + [emmy.env :as e :refer [->infix simplify Lagrange-equations literal-function]] |
13 | 13 | [emmy.mechanics.lagrange :as lg] |
| 14 | + [emmy.expression.render :as r :refer [->infix]] |
14 | 15 | [civitas.repl :as repl])) |
15 | 16 |
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16 | 17 | ;; Elemetary introduction to Emmy, taken from the first pages of the open-access book |
17 | 18 | ;; [Functional Differential Geometry (FDG)](https://mitpress.mit.edu/9780262019347/functional-differential-geometry/). |
18 | 19 | ;; The code snippets are executable, copy-paste them to the sidebar of the page. |
19 | 20 |
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20 | | -;; The Emmy maintainer, Sam Ritchie, wrote the source for this page, namely the |
| 21 | +;; The [Emmy]((https://emmy.mentat.org)) maintainer, [Sam Ritchie](https://roadtoreality.substack.com/), wrote the source for this page, namely the |
21 | 22 | ;; [LaTex version of FDG](https://github.com/mentat-collective/fdg-book/blob/main/scheme/org/prologue.org). |
22 | 23 |
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23 | 24 | ^:kindly/hide-code |
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184 | 185 |
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185 | 186 | ;; By thinking computationally we have reformulated the Lagrange equations into a |
186 | 187 | ;; form that is explicit enough to specify a computation. We could convert it into |
187 | | -;; a program for any symbolic manipulation program because it tells us /how/ to |
| 188 | +;; a program for any symbolic manipulation program because it tells us *how* to |
188 | 189 | ;; manipulate expressions to compute the residuals of Lagrange’s equations for a |
189 | 190 | ;; purported solution path.[fn:2] |
190 | 191 |
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319 | 320 |
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320 | 321 | ;; [note by MAK: the following does not work in the sidebar because I could not get |
321 | 322 | ;; `literal-function` to work. |
322 | | -;; As a remedy, I have an [alternative execution environment](https://kloimhardt.github.io/blog/html/sicmutils-as-js-book-part1.html)] |
| 323 | +;; As a remedy, I have an [alternative execution environment](https://kloimhardt.github.io/blog/html/sicmutils-as-js-book-part1.html) ] |
323 | 324 |
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324 | 325 | (->infix |
325 | 326 | (simplify |
326 | | - (((e/Lagrange-equations (lg/L-harmonic 'm 'k)) |
327 | | - (e/literal-function 'x)) |
| 327 | + (((Lagrange-equations (lg/L-harmonic 'm 'k)) |
| 328 | + (literal-function 'x)) |
328 | 329 | 't))) |
329 | 330 |
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330 | 331 | ;; If this residual is zero we have the Lagrange equation for the harmonic |
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