From 5defb6821f666313f533a1e34c1329e75dae1c37 Mon Sep 17 00:00:00 2001 From: Permondes Date: Sun, 25 Feb 2024 20:09:43 +0100 Subject: [PATCH] Application: Falling Mass Application: Falling Mass Technical: - Helper: Limit Integral to positive values; - Scaling by analyzing the differential equation --- AESL/TP1 07.19 Falling Mass.AESL | 55 +++++++++++++++++++++++++ Analog Engine Example Applications.odt | Bin 1374138 -> 880481 bytes Analog Engine Technical Topics.odt | Bin 397946 -> 401658 bytes 3 files changed, 55 insertions(+) create mode 100644 AESL/TP1 07.19 Falling Mass.AESL diff --git a/AESL/TP1 07.19 Falling Mass.AESL b/AESL/TP1 07.19 Falling Mass.AESL new file mode 100644 index 0000000..d73ae03 --- /dev/null +++ b/AESL/TP1 07.19 Falling Mass.AESL @@ -0,0 +1,55 @@ +IDENTIFICATION DIVISION +PROGRAM-ID FallingParticle +VERSION 20240225 +COMMENT Calculate the deflection from the vertical caused by the Earth's rotation of a particle falling freely from rest from a height h. +COMMENT Differential Equations: +COMMENT x''=-bz'+ay' # x-axis is along latitude, directed to east +COMMENT y''=-ax' # y-axis is along longitude, directed to north +COMMENT z''=-g+ax' # z-axis is perpendicular to the surface of earth +COMMENT g: gravitational acceleration = 9,81 m/s² +COMMENT a: 2*omega*sin(phi) +COMMENT b: 2*omega*cos(phi) +COMMENT omega: rotation velocity of the earth = 2*pi/day +COMMENT phi: Latitude of location (0-90°) +COMMENT Initial Condition: z(0)=h +COMMENT The full solution requires 6 INTEGRATORs, Anabrid-THAT just has 5. The deflection to longitude (y) is neglegible and can be omitted (marked #*). +COMMENT It could also be solved in a separated algorithm omitting x. + +ENVIRONMENT DIVISION +ENGINE Anabrid-THAT +TIMEBASE 1ms +REQUIRES COEFFICIENT 5, INTEGRATOR 5, SUMMER 1, INVERTER 1 + +DATA DIVISION +OUTPUT OUTPUT.X x +OUTPUT OUTPUT.Y y +OUTPUT OUTPUT.Z z +COEFFICIENT.1 AY # 2*2pi/day*sin(phi) +COEFFICIENT.2 AX # = AY +COEFFICIENT.3 B # 2*2pi/day*cos(phi) +COEFFICIENT.4 G # gravitational acceleration = 0,981 da-m/s² +COEFFICIENT.5 H # height h [da-m] + +PROGRAM DIVISION +-1 -> COEFFICIENT.H -> -h + +-bz',ay' -> INTEGRATOR -> -x' # Input is x'' +-x' -> INTEGRATOR -> x + +y'' -> INTEGRATOR -> -y' +#* -y' -> INTEGRATOR -> y + +z'' -> INTEGRATOR -> -z' +-z', IC:-h, SJ:limiter -> INTEGRATOR -> z +CAT:z -> DIODE -> limiter # limit z to >= 0 + +-x' -> COEFFICIENT.AX -> -ax'=y'' +-y' -> COEFFICIENT.AY -> -ay' +-ay' -> INVERTER -> ay' +-z' -> COEFFICIENT.B -> -bz' ++1 -> COEFFICIENT.G -> g +-ax', g -> SUMMER -> -g+ax'=z'' + +OPERATION DIVISION +MODE REPEAT +OP-TIME 7,3ms diff --git a/Analog Engine Example Applications.odt b/Analog Engine Example Applications.odt index de6564b820f22eace882849810167160ff8da8d0..934e710d2e406f3f7323c00e9e78404c494d9bc5 100644 GIT binary patch delta 246417 zcmZTu1z1$w)29Sfa_R0a=?3ZUZs`VT$)&q%X{5WQOIo_Sq+7bf5ApSl|Hre>a?jj3 zbEeLmy?1_1$4YA}tnl(ukWi>#V6b3dyGa@`@RE?v|3JuY0L*$~Q$Q`m%dkTjfR$(o z0DwL&qQZebYofrukWUd%F+uJY02I*4HvrZP>8l0+3*=z|pnMrsNuy$czFGiC|1E|5 zKewJ`o}s=09fPC(mihNm@AiK!WeNCA{v#IvI|U04Nw(SlC}?fI2## z)o^P2C;=P4cSs`FX`S{nS5Qq&=#yi z>i9~ri?g-a^i2|+ZaPl_noXqHHkPgc*|N>CJl5ioeJsgbepbEWsFmD z2a9GisR9tbb0E04s7KOFSub`r`s6bvzdQTPvJBrZfta9ZY$$9u9u#lA&n~Ay&{Cj_ z@jWD0?CXRG>Pk)*|MZY7t=xLg$M@8-fbYhq2w8RTR!QWrdI#o4^|s;?LJD2{E?!Wh zQbL!I@=`Fcq$HcC&0t_)P~c!-zr**(?w7cIbOEG5!2A_a&`Xfy?EtjDV_*lM`JX6u z*a7(eacGA9uQ2~NB){emcB8_@Rlxj?#!FnEIe*9XB{nPe|Bm@@DSw6KUlDxf0)WO0 z0f7HRsy^QVQ1KF<`YdtO{@;;$ks2<8`ojNr#CcydJ(WiNeZeS$`djxu+?2oX|4PhJ 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