AESL/MassOnSphere.AESL

   1 IDENTIFICATION DIVISION
   2 PROGRAM-ID MassOnSphere
   3 VERSION 20240124
   4 COMMENT A mass m rests at the apex on a fixed sphere with radius a.
   5 COMMENT With a slight displacement, it slides down the sphere without friction
   6 COMMENT x'' = C1*x*y - C3*x
   7 COMMENT y'' = C2*y*y - C4*y - g
   8 COMMENT Scaling: measuring distances in dm (10¹ m)
   9 COMMENT Initial condition: slightly off the top of the sphere to get the mass rolling.
  10 COMMENT    Note: x0 is a function of y0 with x0² + y0² = a²
  11 COMMENT    Note: ICs have to be negative as the integrator is inverting
  12
  13 ENVIRONMENT DIVISION
  14 ENGINE Anabrid-THAT
  15 TIMEBASE 1ms
  16 REQUIRES COEFFICIENT 7
  17 REQUIRES INTEGRATOR 4
  18 REQUIRES MULTIPLIER 2
  19 REQUIRES INVERTER 4
  20 REQUIRES SUMMER 2
  21
  22 DATA DIVISION
  23 OUTPUT OUTPUT.X x
  24 OUTPUT OUTPUT.Y y
  25 # Example values based on a=1
  26 COEFFICIENT.1 3g/a² for xy e.g. 2,943
  27 COEFFICIENT.2 3g/a² for y²
  28 COEFFICIENT.3 2g/a  for x  e.g. 1,962
  29 COEFFICIENT.4 2g/a  for y
  30 COEFFICIENT.5 g            e.g. 0,981
  31 COEFFICIENT.6 a initial condition y e.g. 0,957
  32 COEFFICIENT.7 0 initial condition x, slightly above 0 to start motion, e.g. 0,290
  33
  34 PROGRAM DIVISION
  35 -1 -> COEFFICIENT.5 -> -g
  36 -1 -> COEFFICIENT.6 -> -y0
  37 -1 -> COEFFICIENT.7 -> -x0
  38
  39 x'' -> INTEGRATOR.1 -> -x'
  40 -x', IC:-x0 -> INTEGRATOR.2 -> x
  41 y'' -> INTEGRATOR.3 -> -y'
  42 -y', IC:-y0 -> INTEGRATOR.4 -> y
  43 x,y -> MULTIPLIER.1 -> x*y
  44 y,y -> MULTIPLIER.2 -> y^2
  45 x*y -> COEFFICIENT.1 -> 3g/a²*x*y/10
  46 y^2 -> COEFFICIENT.2 -> 3g/a²*y^2/10
  47 x -> COEFFICIENT.3 -> 2g/a*x/10
  48 y -> COEFFICIENT.4 -> 2g/a*y/10
  49 2g/a*x/10 -> INVERTER.1 -> -2g/a*x/10
  50 2g/a*y/10 -> INVERTER.2 -> -2g/a*y/10
  51 10:3g/a²*x*y/10, 10:-2g/a*x/10 -> SUMMER.1 -> -x''
  52 -x'' -> INVERTER.3 -> x''
  53 10:3g/a²*y^2/10, 10:-2g/a*y/10, 1:-g -> SUMMER.2 -> -y''
  54 -y'' -> INVERTER.4 -> y''
  55
  56 OPERATION DIVISION
  57 MODE REPEAT
  58 OP-TIME 0,024 # after that, the mass would jump off the sphere, which is not included in this model