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 = 9,81 m/s²
COEFFICIENT.5 H  # height h

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