Xah Talk Show 2024-07-23 Ep565, Wolfram Language, Code Cycloid Animation

• Wolfram Language Tutorial
• Visual Dictionary of Special Plane Curves
• Cycloid

(* 2024-07-23
Generate a sequence of images of a circle rolling on a line.
A point on the rim of circle traces out a curve called cycloid.
 *)

ListAnimate[
Table[
Graphics[
{
 Circle[ {t,1},1],
Red, Point[{t - Sin[t], 1 - Cos[t]}],
Line[ {{t,1}, {t - Sin[t], 1 - Cos[t]}} ],
Pink, Table[ Point[{x - Sin[x], 1 - Cos[x]}], {x, 0, t, 0.1} ]
},
 Axes -> True,
 PlotRange -> {{-1, 6}, {-0.5, 2.5}}
] ,
{t, 0, 2 Pi, 0.1}
 ]
 ]