permondes.de Git - Analog_Engine.git/blob - scripts/Gravity-2-dimensional.LACE

1 # Gravity–2-dimensional.LACE

3 # The small mass m moves within the gravitational potential of a mass M.

4 # The situation is analysed in polar coordinates.

6 # r'' = r * phi'^2 - gamma*M/r^2

7 # phi'' = -2* r' / r * phi'

9 include CompoundFunctions.LACE # idivide

11 coefficient(1): +1 -> r0' # -1 to move initially towards M, +1 to move away from it

12 coefficient(2): -1 -> -r0 # initial distance of m to M

13 coefficient(3): +1 -> phi0'

14 coefficient(4): -1 -> -phi0

15 coefficient(5): +1 -> gamma*M

17 iintegrate r*phi'^2, -gamma*M/r^2 -> -r' # input is r''

18 IC: r0'

19 iintegrate -r' -> r

20 IC: -r0

22 iintegrate -r'/r*phi', -r'/r*phi' -> -phi' # input is phi''

23 IC: phi0'

24 iintegrate -phi' -> phi

25 IC: -phi0

27 multiply r, -phi' -> -r*phi'

28 multiply -r*phi', -phi' -> r*phi'^2

29 multiply r, r -> r^2

30 idivide gamma*M, r^2 -> -gamma*M/r^2

32 idivide -r', -r*phi' -> r'/r*phi'

33 invert r'/r*phi' -> -r'/r*phi'

35 output(x): r # distance

36 output(y): phi # angle