Catenary Involute

Author

Eric W. Weisstein
March 16, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneCurves/CatenaryInvolute.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/CatenaryInvolute.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Curve

FullSimplify[Involute[{t,Cosh[t]},t]]

Plot

g=InvolutePlot[{t,Cosh[t]},{t,0,2},AspectRatio->Automatic][[1]];

Show[Graphics[{
g,
{
Dashing[{.02}],g/.Line[x_]:>Line[{-#[[1]],#[[2]]}&/@x]
}
}],Axes->True,Ticks->None,
AspectRatio->Automatic
]

Animation

Off[ParametricPlot::"ppcom"]

movie=InvoluteMovie[{t,Cosh[t]},{t,2,0,-.1},{-2,2},
PlotRange->{{-2,2},{0,3}},
AspectRatio->Automatic]

Animated GIF

<<Utilities`GIF`;

Export[gifs<>"catinv.gif",movie]//Timing

Show[Take[movie,{1,20,4}]]