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1 # FallingParticle, VERSION 20240225
2 # Calculate the deflection from the vertical caused by the Earth's rotation of a particle falling freely from rest from a height h.
3 # Differential Equations:
4 # x''=-bz'+ay' # x-axis is along latitude, directed to east
5 # y''=-ax' # y-axis is along longitude, directed to north
6 # z''=-g+ax' # z-axis is perpendicular to the surface of earth
7 # g: gravitational acceleration = 9,81 m/s²
8 # a: 2*omega*sin(phi)
9 # b: 2*omega*cos(phi)
10 # omega: rotation velocity of the earth = 2*pi/day
11 # phi: Latitude of location (0-90°)
12 # Initial Condition: z(0)=h
13 # The full solution requires 6 INTEGRATORs, Anabrid-THAT just has 5. The deflection to longitude (y) is neglegible and can be omitted (marked #*).
14 # It could also be solved in a separated algorithm omitting x.
15
16 coefficient(1): a_y
17 coefficient(2): a_x
18 coefficient(3): b
19 coefficient(4): +1 -> g
20 coefficient(5): -1 -> -h
21
22 iintegrate (-bz', ay') -> -x' # Input is x''
23 iintegrate (-x') -> x
24
25 iintegrate (y'') -> -y'
26 iintegrate (-y') -> y
27
28 iintegrate (z'') -> -z'
29 iintegrate (-z') -> z:
30 IC: -h
31 limit: GT0 # via z to cathode of diode to SJ
32
33 -x' * a_x -> -ax'
34 y'' = -ax'
35 -y' * a_y -> ay'
36 invert (-ay') -> ay'
37 -z' * b -> -bz'
38 isum(-ax', g) -> z'' # gives -g+ax'
39
40 # x -> output (x)
41 # y -> output (y)
42 # z -> output (z)
43
44 #OP-TIME 7,3ms