Applications: Longitudinal oscillating chains; PDEs

[Analog_Engine.git] / scripts / TP1 09.27 Bead on Cycloid.DELACE

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-# A bead glides frictionless on a wire that has the shape of a cycloid 
-# g is the gravitational acceleration 9,81 m/s²
-# a is the radius of the rolling circle (see Bronstein/Semendjajew p. 91)
-# 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
-
-iintegrate mu'' -> -mu'
-   IC: mu0'
-iintegrate -mu' -> mu
-   IC: -mu0
-invert mu -> -mu
--mu * g/4a -> -g/4a*mu
-mu'' = -g/4a*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
-
-# calculating y
-multiply (mu, mu) -> mu^2
-mu^2 * 4ay -> 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
-
-# display mu, so the sinus
-output(z): mu