# equation of motion:
# mu'' = - g/4a * mu, with mu = sin(phi/2) and phi a parameter of the cycloid
-coefficient(1): g/4a
-coefficient(2): 1 -> mu0'
-coefficient(3): -1 -> -mu0
-coefficient(4): 4ax
-coefficient(5): 4ay # same as 4ax
+alias coefficient.1 g/4a
+coefficient.2 (+1) -> mu0'
+coefficient.3 (-1) -> -mu0
+alias coefficient.4 4ax
+alias coefficient.5 4ay # same as 4ax
iintegrate mu'' -> -mu'
IC: mu0'
iintegrate -mu' -> mu
IC: -mu0
invert mu -> -mu
--mu * g/4a -> -g/4a*mu
-mu'' = -g/4a*mu
+coefficient.g/4a (-mu) -> -g/4a*mu
+assign -g/4a*mu -> mu''
# the following is for displaying the cycloid in x-y space
# calculating x (NB: this includes some unacceptable approximations)
-mu * 4ax -> 4a*mu
-output(x): 4a*mu
+coefficient.4ax (mu) -> 4a*mu
+output(4a*mu) -> out.x
# calculating y
multiply mu, mu -> mu^2
-mu^2 * 4ay -> 4ay*mu^2
+coefficient.4ay (mu^2) -> 4ay*mu^2
isum 4a*mu^2 -> -2a*mu^2 # just serves to devide by 2 because we need 2a instead of 4a
/2
invert -2a*mu^2 -> 2a*mu^2
-output(y): 2a*mu^2
+output(2a*mu^2) -> out.y
# display mu, so the sinus
-output(z): mu
+output(mu) -> out.z