| | 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 |
| | 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 -> -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'' |
| | 55 | |
| | 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 |
projects / Analog_Engine.git / blame_incremental