Function Repository Resource:

# EpicyclePlot

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 ri. ResourceFunction["EpicyclePlot"][{{r1,f1},{r2,f2},…},t] plots the epicycle with component radii ri and frequencies fi. 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 ϕi. 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:

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

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### Options (3)

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

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

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All Graphics options are supported:

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### Neat Examples (1)

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

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Jon McLoone

## Version History

• 3.0.0 – 07 December 2020
• 2.0.0 – 29 October 2020
• 1.0.0 – 15 October 2019