scripts/Gravity-2-dimensional.LACE

   1 # Gravity–2-dimensional.LACE
   2
   3 # The small mass m moves within the gravitational potential of a mass M.
   4 # The situation is analysed in polar coordinates.
   5
   6 # r'' = r * phi'^2 - gamma*M/r^2
   7 # phi'' = -2* r' / r * phi'
   8
   9 include CompoundFunctions.LACE   # idivide
  10
  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
  16
  17 iintegrate r*phi'^2, -gamma*M/r^2 -> -r' # input is r''
  18    IC: r0'
  19 iintegrate -r' -> r
  20   IC: -r0
  21
  22 iintegrate -r'/r*phi', -r'/r*phi' -> -phi' # input is phi''
  23   IC: phi0'
  24 iintegrate -phi' -> phi
  25   IC: -phi0
  26
  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
  31
  32 idivide -r', -r*phi' -> r'/r*phi'
  33 invert r'/r*phi' -> -r'/r*phi'
  34
  35 output(x): r      # distance
  36 output(y): phi    # angle