| | 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 = 9,81 m/s² |
| | 31 | COEFFICIENT.5 H # height h |
| | 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 |
projects / Analog_Engine.git / blame_incremental