Function Repository Resource:

EpicyclePlot

Source Notebook

Plot the composition of cycles having different radii, frequencies and phases

Contributed by: Jon McLoone

ResourceFunction["EpicyclePlot"][{r₁,r₂,…},t]

plots the epicycle where the component cycle of frequency i has radius r_i.

ResourceFunction["EpicyclePlot"][{{r₁,f₁},{r₂,f₂},…},t]

plots the epicycle with component radii r_i and frequencies f_i.

ResourceFunction["EpicyclePlot"][{{r₁,f₁,ϕ₁},{r₂,f₂,ϕ₂},…},t]

plots the epicycle with the given component radii and frequencies, with relative phases given by the ϕ_i.

ResourceFunction["EpicyclePlot"][data,t,{t₀,t₁}]

plots the epicycle given by data at time t together with the path traced between time t₀ and t₁.

Details and Options

ResourceFunction["EpicyclePlot"] accepts all the options of Graphics, together with "PathStyle", "SpokeStyle", "CircleStyle" and "PointStyle" that determine the appearance of the resulting plot.

Examples

Basic Examples (2)

A plot of epicycles with radii 1, 0.2 and 0.1 and frequencies of 1, 2 and 3:

In[1]:=

Out[1]=

Replot, also showing the path traced out by the composition between t=0 and t=2π:

In[2]:=

$ResourceFunction["EpicyclePlot"][{1, 0.2, 0.1}, 0.5, {0, 2 \[Pi]}]$

Out[2]=

Options (3)

The style of the four elements of an EpicyclePlot are controlled with "PathStyle", "SpokeStyle", "CircleStyle" and "PointStyle":

In[3]:=

$ResourceFunction[ "EpicyclePlot"][{{1, 1}, {0.2, 7}}, 0.5, {0, 2 \[Pi]}, "SpokeStyle" -> None, "CircleStyle" -> None, "PointStyle" -> None]$

Out[3]=

The options "PathStyle", "SpokeStyle", "CircleStyle" and "PointStyle" accept style directives:

In[4]:=

$ResourceFunction[ "EpicyclePlot"][{{1, 1}, {0.2, 4}}, 0.5, {0, 2 \[Pi]}, "SpokeStyle" -> Blue, "CircleStyle" -> Directive[Gray, Dashed], "PointStyle" -> PointSize[0.04], "PathStyle" -> Thickness[0.01]]$

Out[4]=

All Graphics options are supported:

In[5]:=

$ResourceFunction[ "EpicyclePlot"][{{1, 1}, {0.2, 7}}, 0.5, {0, 2 \[Pi]}, Background -> LightBlue]$

Out[5]=

Neat Examples (1)

Explore loci of epicycles of radius 1/3, 1/2, 1:

In[6]:=

$Manipulate[ ResourceFunction["EpicyclePlot"][{{1/3, f1}, {1/2, f2}, {1, f3}}, 0, {0, 2 \[Pi]}, "CircleStyle" -> None, "PointStyle" -> None, "SpokeStyle" -> None], {{f1, 17}, -20, 20}, {{f2, -7}, -20, 20}, {{f3, -1}, -20, 20}]$