From: Permondes <machen@permondes.de>
Date: Mon, 25 Nov 2024 20:55:10 +0000 (+0100)
Subject: Focus on potential fields
X-Git-Url: https://permondes.de/gitweb/Analog_Engine.git/commitdiff_plain/e25ae3805c3f6ab36385c2d04bbf148736184386

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
---

diff --git a/Analog Engine Example Applications.odt b/Analog Engine Example Applications.odt
index 4f83903..0a43759 100644
Binary files a/Analog Engine Example Applications.odt and b/Analog Engine Example Applications.odt differ
diff --git a/Language for Analog Computing Engines.odt b/Language for Analog Computing Engines.odt
index 4da5af0..cad656a 100644
Binary files a/Language for Analog Computing Engines.odt and b/Language for Analog Computing Engines.odt differ
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
+#