From 48debccd2fb1ede90115dd471fae71b2761e1299 Mon Sep 17 00:00:00 2001 From: Permondes Date: Wed, 5 Jun 2024 21:32:52 +0200 Subject: [PATCH] Application: Bead glides on cycloidic wire Application: Bead glides on cycloidic wire DELACE: added operation output, division in isum --- Analog Engine Example Applications.odt | Bin 951387 -> 1021102 bytes ...on Language for Analog Circuit Engines.odt | Bin 36677 -> 37088 bytes scripts/TP1 09.26 rope over table edge.DELACE | 2 +- scripts/TP1 09.27 Bead on Cycloid.DELACE | 35 ++++++++++++++++++ 4 files changed, 36 insertions(+), 1 deletion(-) create mode 100644 scripts/TP1 09.27 Bead on Cycloid.DELACE diff --git a/Analog Engine Example Applications.odt b/Analog Engine Example Applications.odt index 083e01d6348d0f6b1d8560a950546a85abbca1b2..0fba40a970da3e552a96d3c1acf019d7261aae51 100644 GIT binary patch delta 134025 zcmcG$byU^O_Xf(LK@Q#B-QCg+(p{2@w3G-OKtM_w4j^43CEeXfmo$RX-6?VpnD6_2 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zz*4_i$J>|Sc8>i@4Xk&ZLJ1Tghc=?9o5X8cv5e;hp8ZsWngK>tHHKMA{iO=46%Jl+ zMZ2jG$DECYn)~nvPd;B8>n^H9?Cf2L8s z-N_g6R~eySr^gV7mYHr|Y3Q(Gp23&;gJt(!cK_i`I-%(O zYc_ww(TP`VmMEOK#yxv>MOpuxOvc(nF5KCMk;c0^9;|U*vZBjxr|E-c)qB+^rz(0M z=9+(Zm8NP`Rq(#h#aVLJW|ta#B&szR`Z?=4ONyFgI`+0R>AYWkX@igHdO=}D?F4ha zimP#ly!fpSg%=!Gd!Kepul~{g{Qom8iu#X>TZk-<)$;aIJYTlZBWj^b_U-RePi&tq z-fkpn-hHFae|7Li@i+Xbny0Sr`=k}5)Dx`EnX-mMutqRRL|4#5SF++@t^UlJ->m{X zCv=8c^n|wWJvHO%KjRY2^nOdKi|I_N$L-Be}uK!Py z(!KAUnXr%TDdfKG?ngHtKa*r&Fusa5bF`VMJD-tRvTg6=k{)9){k~6n^3fiV$qr0h zyo^jD3?d8+91IK~6+jur=E>g~WzobPd!-q7PTtQbKY30c7ubwdJ<^OHC$};xVya}) zW}NKDC^wl4suXA_Q!?Yk2V#@;7}>BWp9z$cn_Sb&r2uq71ZcT249LS6VEQ8CWWiot znC(n_OcOH|pvJ)_$xQpr`9Ox;&W+}L!3eynn|X3ozlJCv89u#wzPCnQ#4OWAC zGdZ#%&&j|0)$2j#fT!r7Gjv?YN*J!kFfbICROX}>>s93D1b9P&7V5MJu7uSCX1nf=%NT?{;oopkGv3fVPUF=#1)|EZ8kR`P2jfwo_do82~5Jwn_j1 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 -- 2.39.2