# FallingParticle, VERSION 20240225
# Calculate the deflection from the vertical caused by the Earth's rotation of a particle falling freely from rest from a height h.
# Differential Equations:
#    x''=-bz'+ay' # x-axis is along latitude,  directed to east
#    y''=-ax'     # y-axis is along longitude, directed to north
#    z''=-g+ax'   # z-axis is perpendicular to the surface of earth
#    g: gravitational acceleration = 9,81 m/s²
#    a: 2*omega*sin(phi)
#    b: 2*omega*cos(phi)
#    omega: rotation velocity of the earth = 2*pi/day
#    phi: Latitude of location (0-90°)
#    Initial Condition: z(0)=h
# The full solution requires 6 INTEGRATORs, Anabrid-THAT just has 5. The deflection to longitude (y) is neglegible and can be omitted (marked #*).
# It could also be solved in a separated algorithm omitting x.

coefficient(1): a_y
coefficient(2): a_x
coefficient(3): b
coefficient(4): +1 -> g
coefficient(5): -1 -> -h

iintegrate (-bz', ay') -> -x' # Input is x''
iintegrate (-x') -> x

iintegrate (y'') -> -y'
iintegrate (-y') -> y

iintegrate (z'') -> -z'
iintegrate (-z') -> z:
   IC: -h
   limit: GT0 # via z to cathode of diode to SJ 
   
-x' * a_x -> -ax'
y'' = -ax'
-y' * a_y -> ay'
invert (-ay') -> ay'
-z' * b -> -bz'
isum(-ax', g) -> z'' # gives -g+ax'

# x -> output (x)
# y -> output (y)
# z -> output (z)

#OP-TIME 7,3ms