permondes.de Git - Analog_Engine.git/blob - scripts/TP1 07.19 Falling Mass.LACE

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.

16 coefficient(1): a_y

17 coefficient(2): a_x

18 coefficient(3): b

19 coefficient(4): +1 -> g

20 coefficient(5): -1 -> -h

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

23 iintegrate (-x') -> x

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

26 iintegrate (-y') -> y

28 iintegrate (z'') -> -z'

29 iintegrate (-z') -> z:

30 IC: -h

31 limit: GT0 # via z to cathode of diode to SJ

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'

40 # x -> output (x)

41 # y -> output (y)

42 # z -> output (z)

44 #OP-TIME 7,3ms