From: Permondes Date: Sun, 25 Feb 2024 19:09:43 +0000 (+0100) Subject: Application: Falling Mass X-Git-Url: https://permondes.de/gitweb/Analog_Engine.git/commitdiff_plain/5defb6821f666313f533a1e34c1329e75dae1c37?ds=sidebyside;hp=1820e06bd06c1df8c4cbfd882735c9f937cc0029 Application: Falling Mass Application: Falling Mass Technical: - Helper: Limit Integral to positive values; - Scaling by analyzing the differential equation --- 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 de6564b..934e710 100644 Binary files a/Analog Engine Example Applications.odt and b/Analog Engine Example Applications.odt differ diff --git a/Analog Engine Technical Topics.odt b/Analog Engine Technical Topics.odt index c151369..d3efb95 100644 Binary files a/Analog Engine Technical Topics.odt and b/Analog Engine Technical Topics.odt differ