From e25ae3805c3f6ab36385c2d04bbf148736184386 Mon Sep 17 00:00:00 2001 From: Permondes Date: Mon, 25 Nov 2024 21:55:10 +0100 Subject: [PATCH] Focus on potential fields Applications: Focus on potential fields; mathematical basics; Comet on parabolic orbit using differential equations; systems with variable mass; geostationary satellite LACE: define: some items are optional; CompoundFunctions.LACE --- Analog Engine Example Applications.odt | Bin 1554177 -> 1816556 bytes Language for Analog Computing Engines.odt | Bin 62323 -> 56560 bytes scripts/CompoundFunctions.LACE | 1 + .../Gravity-1-dimensional.LACE | 0 scripts/Gravity-2-dimensional.LACE | 36 ++++++++++++++++++ scripts/THAT.LACE | 2 + 6 files changed, 39 insertions(+) rename "scripts/Gravity \342\200\223 1-dimensional.LACE" => scripts/Gravity-1-dimensional.LACE (100%) create mode 100644 scripts/Gravity-2-dimensional.LACE create mode 100644 scripts/THAT.LACE diff --git a/Analog Engine Example Applications.odt b/Analog Engine Example 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zX!o7YALIv())0L{=Gm;+dDkV&BQD(@0X2rW=DC>#hJ2zZD$0EjnC2$28uKauz~)9?RA)Ib0C`Tfj4 zeEff(=V#ud{=tw?NYA0Sg@=I11u@UEQvA7+qrXsyWdQ;4=OFkOyu{!0IR*$FlL-A^ zW&R6YAZwNwO3(w;HcR#Q{*$>hy$EOsh;SkZ2;Bd;zsxgXj`}ZhMa`|%FW5Jzg5Wnf zl>d=No3;7i-B64AQsVfB+J4j*{2mW8iEX)x@FI5Kn4rMP`|T5-V6UIlKI9K<%3!m{;BhS&*(qfO!Oz{ zb%E}$djD@Bm!F`3EE3dzy3)UT((ff=sKTG1=tYLVrvG8re}d3+@Id>E|DZm+ED}Qz z7J`VESpQ0Ve3Q^D1X(RH{U7#AAt)`I;{THIP$B4PiQ)gF7F5w&aU>w)Wu(6u+AR}9 g2^4{%mj9{ke;)?O|85%upae9!ObT~#@aO7(0TL4A!~g&Q diff --git a/scripts/CompoundFunctions.LACE b/scripts/CompoundFunctions.LACE index e2a7cef..d3329ed 100644 --- a/scripts/CompoundFunctions.LACE +++ b/scripts/CompoundFunctions.LACE @@ -1,3 +1,4 @@ +# CompoundFunctions.LACE # collection of compound functions which can be realized with THAT # Open Amplifier diff --git "a/scripts/Gravity \342\200\223 1-dimensional.LACE" b/scripts/Gravity-1-dimensional.LACE similarity index 100% rename from "scripts/Gravity \342\200\223 1-dimensional.LACE" rename to scripts/Gravity-1-dimensional.LACE diff --git a/scripts/Gravity-2-dimensional.LACE b/scripts/Gravity-2-dimensional.LACE new file mode 100644 index 0000000..92a36fb --- /dev/null +++ b/scripts/Gravity-2-dimensional.LACE @@ -0,0 +1,36 @@ +# Gravity–2-dimensional.LACE + +# The small mass m moves within the gravitational potential of a mass M. +# The situation is analysed in polar coordinates. + +# r'' = r * phi'^2 - gamma*M/r^2 +# phi'' = -2* r' / r * phi' + +include CompoundFunctions.LACE # idivide + +coefficient(1): +1 -> r0' # -1 to move initially towards M, +1 to move away from it +coefficient(2): -1 -> -r0 # initial distance of m to M +coefficient(3): +1 -> phi0' +coefficient(4): -1 -> -phi0 +coefficient(5): +1 -> gamma*M + +iintegrate r*phi'^2, -gamma*M/r^2 -> -r' # input is r'' + IC: r0' +iintegrate -r' -> r + IC: -r0 + +iintegrate -r'/r*phi', -r'/r*phi' -> -phi' # input is phi'' + IC: phi0' +iintegrate -phi' -> phi + IC: -phi0 + +multiply r, -phi' -> -r*phi' +multiply -r*phi', -phi' -> r*phi'^2 +multiply r, r -> r^2 +idivide gamma*M, r^2 -> -gamma*M/r^2 + +idivide -r', -r*phi' -> r'/r*phi' +invert r'/r*phi' -> -r'/r*phi' + +output(x): r # distance +output(y): phi # angle diff --git a/scripts/THAT.LACE b/scripts/THAT.LACE new file mode 100644 index 0000000..81228ff --- /dev/null +++ b/scripts/THAT.LACE @@ -0,0 +1,2 @@ +# definitions of functions available on the Anabrid-THAT +# -- 2.39.5