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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