scripts/Pendulum.LACE

   1 # Pendulum: Comparing Harmonic Oscillator with 4th order Taylor approximation
   2
   3 ### Taylor 4 approximation: phi'' = - g/r * (phi - 1/6 * phi^3)
   4 # fortunately, the components of orders 0, 2 and 4 are zero
   5
   6 coefficient.1     -> g/r
   7 coefficient.2     -> 1/6   # set to 0,167 or 0 (for harmonic solution)
   8 coefficient.3(-1) -> -phi0
   9
  10 iintegrate phi'' -> -phi'
  11 iintegrate -phi' -> phi
  12   IC: -phi0
  13
  14 multiply phi, phi   -> phi^2
  15 multiply phi^2, phi -> phi^3
  16 invert phi^3 -> -phi^3
  17
  18 cmultiply 1/6, -phi^3 -> -1/6*phi^3
  19 isum phi, -1/6*phi^3 -> -(phi-1/6*phi^3)
  20 cmultiply -(phi-1/6*phi^3), g/r -> -g/r*(phi-1/6*phi^3)
  21 assign -g/r*(phi-1/6*phi^3) -> phi''
  22
  23 output phi -> out.x
  24
  25 ### Harmonic oscillator: phi'' = - g/r * phi
  26 coefficient.5     -> g/r_h    # identical to g/r
  27 coefficient.7(-1) -> -phi0_h  # identical to -phi0
  28
  29 iintegrate phi_h'' -> -phi_h'
  30 iintegrate -phi_h' -> phi_h
  31   IC: -phi0_h
  32 invert phi_h -> -phi_h
  33
  34 cmultiply -phi_h, g/r_h -> -g/r*phi_h
  35 assign -g/r*phi_h -> phi_h''
  36
  37 output phi_h -> out.y