permondes.de Git - Analog_Engine.git/blob - 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

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

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''

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

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

34 # display mu, so the sinus

35 output(mu) -> out.z