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 083e01d6348d0f6b1d8560a950546a85abbca1b2..0fba40a970da3e552a96d3c1acf019d7261aae51 100644 (file)
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diff --git a/DEscription Language for Analog Circuit Engines.odt b/DEscription Language for Analog Circuit Engines.odt
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diff --git a/scripts/TP1 09.26 rope over table edge.DELACE b/scripts/TP1 09.26 rope over table edge.DELACE
index efff3eadde4dbaf34229bcb9486eacc0b97745b6..b4695cbc631d1f943cb884d3b55ee7e199176353 100644 (file)
--- 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 (file)
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