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Applications: Longitudinal oscillating chains; PDEs
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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
16coefficient(1): a_y
17coefficient(2): a_x
18coefficient(3): b
19coefficient(4): +1 -> g
20coefficient(5): -1 -> -h
21
22iintegrate (-bz', ay') -> -x' # Input is x''
23iintegrate (-x') -> x
24
25iintegrate (y'') -> -y'
26iintegrate (-y') -> y
27
28iintegrate (z'') -> -z'
29iintegrate (-z') -> z:
30 IC: -h
31 limit: GT0 # via z to cathode of diode to SJ
32
33-x' * a_x -> -ax'
34y'' = -ax'
35-y' * a_y -> ay'
36invert (-ay') -> ay'
37-z' * b -> -bz'
38isum(-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