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 4f83903a1b1c2cc8593373015a693c3e0b55dda1..0a437594ab44757c50eff5c69522692091f15dd0 100644 (file)
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diff --git a/Language for Analog Computing Engines.odt b/Language for Analog Computing Engines.odt
index 4da5af013de0d1ecc0d98d103aeaef6b0771211a..cad656a25de365ab8d52840f33338d002d67d726 100644 (file)
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diff --git a/scripts/CompoundFunctions.LACE b/scripts/CompoundFunctions.LACE
index e2a7cef374340a89e68ffd0d6be7f3bfa2cf1931..d3329ed92fb8ee4673db421fc4c3481e55c8e2db 100644 (file)
--- 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 – 1-dimensional.LACE b/scripts/Gravity-1-dimensional.LACE
similarity index 100%
rename from scripts/Gravity – 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 (file)
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 (file)
index 0000000..81228ff
--- /dev/null
+++ b/scripts/THAT.LACE
@@ -0,0 +1,2 @@
+# definitions of functions available on the Anabrid-THAT
+#