Re: Tracing a Cycloid
- To: mathgroup at smc.vnet.net
- Subject: [mg84936] Re: Tracing a Cycloid
- From: sashap <pavlyk at gmail.com>
- Date: Sun, 20 Jan 2008 03:36:55 -0500 (EST)
- References: <fmsldf$j30$1@smc.vnet.net>
On Jan 19, 5:03 am, Narasimham <mathm... at hotmail.com> wrote:
> Cycloid[t_]:=Show[ Graphics[
> {Circle[{t, 1}, 1], Circle[{t, 0}, .04],Circle[{t, 1}, .
> 02],Disk[{t-Sin[t],1-Cos[t]},.1 ]}],
> AspectRatio -> Automatic,PlotRange->{{-1,7.2},{-.
> 1,2.1}}] ;
>
> Do[Cycloid[v],{v,-1,8.,.1}];
>
> How to leave behind the mark/trace of the black point on rolling
> circle periphery while tracing out the cycloid?
>
> Also, how to modify this using Animate command for same animation
> tracing effect instead of the Do command?
>
> Thanks for suggestions.
>
> Narasimham
In version 6:
Cycloid[t_] := Show[
ParametricPlot[{x - Sin[x], 1 - Cos[x]}, {x, -1.1, t}],
Graphics[{Circle[{t, 1}, 1], Circle[{t, 0}, .04],
Circle[{t, 1}, 0.02], Disk[{t - Sin[t], 1 - Cos[t]}, .1]}],
AspectRatio -> Automatic, PlotRange -> {{-1, 7.2}, {-0.1, 2.1}}];
Animate[Cycloid[v], {v, 0, 7.0, 0.1}]
Additionally, have a look at
http://demonstrations.wolfram.com/CycloidCurves/
Hope this helps,
Oleksandr