a rope slides frictionlessly down the edge of a table

[Analog_Engine.git] / AESL / TP1 07.19 Falling Mass.AESL

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-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