Animating a moving circle

By Nasser M. Abbasi, oct 10,2009

I saw nice animation of a moving circle and cycloid written by amca01 on the web. It was implemented in sage.

Here is the sage implementation by amca01 and below it is the Mathematica implementation I wrote of the same idea as the above. I also include Mathematica animated gif file.

Sage code:

step = 0.3

v = []

for t in srange(0,2*pi,step):

v.append(circle((t,1),1))

a = animate(v, xmin=-1, ymin=0, xmax=8, ymax=2, figsize=[9,2])

w = []

for t in srange(0,2*pi,step):

w.append(point((t-sin(t),1-cos(t)),pointsize=20))

b = animate(w, xmin=-1, ymin=0, xmax=8, ymax=2, figsize=[9,2])

L = Graphics()

x = []

for t in srange(0,2*pi,step):

L += line([(t-step-sin(t-step),1-cos(t-step)),(t-sin(t),1-cos(t))], rgbcolor=(1,0,0), thickness=2)

x.append(L)

c = animate(x, xmin=-1, ymin=0, xmax=8, ymax=2, figsize=[9,2])

(a+b+c).show()

Here is the Mathematica code

r = 1; step = 0.1;

backgroundAxes = Plot[0, {x, -Pi, 3*Pi},

PlotRange -> {Automatic, {-r/2, 2*r + 0.5}},

AspectRatio -> Automatic];

Animate[Show[{backgroundAxes,

ListPlot[Table[{x - Sin[x], 1 - Cos[x]}, {x, 0, t, step}],

Joined -> True],

Graphics[{PointSize[Large], Red, Point[{t - Sin[t], 1 - Cos[t]}]}],

Graphics[Circle[{t, 1}, r]]}],{t, 0, 2*Pi, step}, AnimationRate -> 5

]

Here is the GIF animation from the Mathematica code

Here is the Mathematica notebook