scripts/TP1 09.27 Bead on Cycloid.LACE

   1 # A bead glides frictionless on a wire that has the shape of a cycloid
   2 # g is the gravitational acceleration 9,81 m/s²
   3 # a is the radius of the rolling circle (see Bronstein/Semendjajew p. 91)
   4 # equation of motion:
   5 #   mu'' = - g/4a * mu, with mu = sin(phi/2) and phi a parameter of the cycloid
   6
   7 alias coefficient.1 g/4a
   8 coefficient.2 (+1) -> mu0'
   9 coefficient.3 (-1) -> -mu0
  10 alias coefficient.4 4ax
  11 alias coefficient.5 4ay # same as 4ax
  12
  13 iintegrate mu'' -> -mu'
  14    IC: mu0'
  15 iintegrate -mu' -> mu
  16    IC: -mu0
  17 invert mu -> -mu
  18 coefficient.g/4a (-mu) -> -g/4a*mu
  19 assign -g/4a*mu -> mu''
  20
  21 # the following is for displaying the cycloid in x-y space
  22 # calculating x (NB: this includes some unacceptable approximations)
  23 coefficient.4ax (mu) -> 4a*mu
  24 output(4a*mu) -> out.x
  25
  26 # calculating y
  27 multiply mu, mu -> mu^2
  28 coefficient.4ay (mu^2) -> 4ay*mu^2
  29 isum 4a*mu^2 -> -2a*mu^2     # just serves to devide by 2 because we need 2a instead of 4a
  30   /2
  31 invert -2a*mu^2 -> 2a*mu^2
  32 output(2a*mu^2) -> out.y
  33
  34 # display mu, so the sinus
  35 output(mu) -> out.z