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1 IDENTIFICATION DIVISION
2 PROGRAM-ID FallingParticle
3 VERSION 20240225
4 COMMENT Calculate the deflection from the vertical caused by the Earth's rotation of a particle falling freely from rest from a height h.
5 COMMENT Differential Equations:
6 COMMENT x''=-bz'+ay' # x-axis is along latitude, directed to east
7 COMMENT y''=-ax' # y-axis is along longitude, directed to north
8 COMMENT z''=-g+ax' # z-axis is perpendicular to the surface of earth
9 COMMENT g: gravitational acceleration = 9,81 m/s²
10 COMMENT a: 2*omega*sin(phi)
11 COMMENT b: 2*omega*cos(phi)
12 COMMENT omega: rotation velocity of the earth = 2*pi/day
13 COMMENT phi: Latitude of location (0-90°)
14 COMMENT Initial Condition: z(0)=h
15 COMMENT The full solution requires 6 INTEGRATORs, Anabrid-THAT just has 5. The deflection to longitude (y) is neglegible and can be omitted (marked #*).
16 COMMENT It could also be solved in a separated algorithm omitting x.
17
18 ENVIRONMENT DIVISION
19 ENGINE Anabrid-THAT
20 TIMEBASE 1ms
21 REQUIRES COEFFICIENT 5, INTEGRATOR 5, SUMMER 1, INVERTER 1
22
23 DATA DIVISION
24 OUTPUT OUTPUT.X x
25 OUTPUT OUTPUT.Y y
26 OUTPUT OUTPUT.Z z
27 COEFFICIENT.1 AY # 2*2pi/day*sin(phi)
28 COEFFICIENT.2 AX # = AY
29 COEFFICIENT.3 B # 2*2pi/day*cos(phi)
30 COEFFICIENT.4 G # gravitational acceleration = 9,81 m/s²
31 COEFFICIENT.5 H # height h
32
33 PROGRAM DIVISION
34 -1 -> COEFFICIENT.H -> -h
35
36 -bz',ay' -> INTEGRATOR -> -x' # Input is x''
37 -x' -> INTEGRATOR -> x
38
39 y'' -> INTEGRATOR -> -y'
40 #* -y' -> INTEGRATOR -> y
41
42 z'' -> INTEGRATOR -> -z'
43 -z', IC:-h, SJ:limiter -> INTEGRATOR -> z
44 CAT:z -> DIODE -> limiter # limit z to >= 0
45
46 -x' -> COEFFICIENT.AX -> -ax'=y''
47 -y' -> COEFFICIENT.AY -> -ay'
48 -ay' -> INVERTER -> ay'
49 -z' -> COEFFICIENT.B -> -bz'
50 +1 -> COEFFICIENT.G -> g
51 -ax', g -> SUMMER -> -g+ax'=z''
52
53 OPERATION DIVISION
54 MODE REPEAT
55 OP-TIME 7,3ms