scripts/TP1 07.19 Falling Mass.DELACE

   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