| | 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 |
projects / Analog_Engine.git / blame_incremental