From: Permondes 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 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