AESL/TP1 07.19 Falling Mass.AESL

   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 = 0,981 da-m/s²
  31 COEFFICIENT.5 H  # height h [da-m]
  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