| 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 |