permondes.de Git - Analog_Engine.git/blob - scripts/TP1 04.10 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 da-m (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

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

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

34 PROGRAM DIVISION

35 -1 -> COEFFICIENT.5 -> -g

36 -1 -> COEFFICIENT.6 -> -y0

37 -1 -> COEFFICIENT.7 -> -x0

39 x'' -> INTEGRATOR -> -x'

40 -x', IC:-x0 -> INTEGRATOR -> x

41 y'' -> INTEGRATOR -> -y'

42 -y', IC:-y0 -> INTEGRATOR -> y

43 x,y -> MULTIPLIER -> x*y

44 y,y -> MULTIPLIER -> 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 -> -2g/a*x/10

50 2g/a*y/10 -> INVERTER -> -2g/a*y/10

51 10:3g/a²*x*y/10, 10:-2g/a*x/10 -> SUMMER -> -x''

52 -x'' -> INVERTER -> x''

53 10:3g/a²*y^2/10, 10:-2g/a*y/10, 1:-g -> SUMMER -> -y''

54 -y'' -> INVERTER -> y''

56 OPERATION DIVISION

57 MODE REPEAT

58 OP-TIME 24ms # after that, the mass would jump off the sphere, which is not included in this model