From: Permondes <machen@permondes.de>
Date: Wed, 5 Jun 2024 19:32:52 +0000 (+0200)
Subject: Application: Bead glides on cycloidic wire
X-Git-Url: https://permondes.de/gitweb/Analog_Engine.git/commitdiff_plain/48debccd2fb1ede90115dd471fae71b2761e1299?hp=6e4089e8217c971c0154c414f5fed5d0807d179e

Application: Bead glides on cycloidic wire

Application: Bead glides on cycloidic wire
DELACE: added operation output, division in isum
---

diff --git a/Analog Engine Example Applications.odt b/Analog Engine Example Applications.odt
index 083e01d..0fba40a 100644
Binary files a/Analog Engine Example Applications.odt and b/Analog Engine Example Applications.odt differ
diff --git a/DEscription Language for Analog Circuit Engines.odt b/DEscription Language for Analog Circuit Engines.odt
index 9f700a9..6332b1e 100644
Binary files a/DEscription Language for Analog Circuit Engines.odt and b/DEscription Language for Analog Circuit Engines.odt differ
diff --git a/scripts/TP1 09.26 rope over table edge.DELACE b/scripts/TP1 09.26 rope over table edge.DELACE
index efff3ea..b4695cb 100644
--- a/scripts/TP1 09.26 rope over table edge.DELACE	
+++ b/scripts/TP1 09.26 rope over table edge.DELACE	
@@ -3,7 +3,7 @@
 
 coefficient(1): 1 -> x0'   # initial speed
 coefficient(2): -1 -> -x0  # initial length of rope already over the edge of the table
-coefficient(3): g/l        # gravity constant (g) devided by the length of the rope (l)
+coefficient(3): g/l        # gravity constant (g) divided by the length of the rope (l)
 
 iintegrate (x'') -> -x':
    IC: x0'
diff --git a/scripts/TP1 09.27 Bead on Cycloid.DELACE b/scripts/TP1 09.27 Bead on Cycloid.DELACE
new file mode 100644
index 0000000..a936c75
--- /dev/null
+++ b/scripts/TP1 09.27 Bead on Cycloid.DELACE	
@@ -0,0 +1,35 @@
+# A bead glides frictionless on a wire that has the shape of a cycloid 
+# g is the gravitational acceleration 9,81 m/s²
+# a is the radius of the rolling circle (see Bronstein/Semendjajew p. 91)
+# equation of motion:
+#   mu'' = - g/4a * mu, with mu = sin(phi/2) and phi a parameter of the cycloid 
+
+coefficient(1): g/4a
+coefficient(2): 1 -> mu0'
+coefficient(3): -1 -> -mu0
+coefficient(4): 4ax
+coefficient(5): 4ay # same as 4ax
+
+iintegrate mu'' -> -mu'
+   IC: mu0'
+iintegrate -mu' -> mu
+   IC: -mu0
+invert mu -> -mu
+-mu * g/4a -> -g/4a*mu
+mu'' = -g/4a*mu
+
+# the following is for displaying the cycloid in x-y space
+# calculating x (NB: this includes some unacceptable approximations)
+mu * 4ax -> 4a*mu
+output(x): 4a*mu
+
+# calculating y
+multiply (mu, mu) -> mu^2
+mu^2 * 4ay -> 4ay*mu^2
+isum 4a*mu^2 -> -2a*mu^2     # just serves to devide by 2 because we need 2a instead of 4a
+  /2
+invert (-2a*mu^2) -> 2a*mu^2 
+output(y): 2a*mu^2
+
+# display mu, so the sinus
+output(z): mu