projects / Analog_Engine.git / blame
| Commit | Line | Data |
|---|---|---|
| 7fbf87e4 P |
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. | |
| 15 | ||
| 16 | coefficient(1): a_y | |
| 17 | coefficient(2): a_x | |
| 18 | coefficient(3): b | |
| 19 | coefficient(4): +1 -> g | |
| 20 | coefficient(5): -1 -> -h | |
| 21 | ||
| 22 | iintegrate (-bz', ay') -> -x' # Input is x'' | |
| 23 | iintegrate (-x') -> x | |
| 24 | ||
| 25 | iintegrate (y'') -> -y' | |
| 26 | iintegrate (-y') -> y | |
| 27 | ||
| 28 | iintegrate (z'') -> -z' | |
| 29 | iintegrate (-z') -> z: | |
| 30 | IC: -h | |
| 31 | limit: GT0 # via z to cathode of diode to SJ | |
| 32 | ||
| 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' | |
| 39 | ||
| 40 | # x -> output (x) | |
| 41 | # y -> output (y) | |
| 42 | # z -> output (z) | |
| 43 | ||
| 44 | #OP-TIME 7,3ms |