Wolfram Function Repository
Instantuse addon functions for the Wolfram Language
Function Repository Resource:
Plot the composition of cycles having different radii, frequencies and phases
ResourceFunction["EpicyclePlot"][{r_{1},r_{2},…},t] plots the epicycle where the component cycle of frequency i has radius r_{i}.  
ResourceFunction["EpicyclePlot"][{{r_{1},f_{1}},{r_{2},f_{2}},…},t] plots the epicycle with component radii r_{i} and frequencies f_{i}.  
ResourceFunction["EpicyclePlot"][{{r_{1},f_{1},ϕ_{1}},{r_{2},f_{2},ϕ_{2}},…},t] plots the epicycle with the given component radii and frequencies, with relative phases given by the ϕ_{i}.  
ResourceFunction["EpicyclePlot"][data,t,{t_{0},t_{1}}] plots the epicycle given by data at time t together with the path traced between time t_{0} and t_{1}. 
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]:= 

Out[2]= 

The style of the four elements of an EpicyclePlot are controlled with "PathStyle", "SpokeStyle", "CircleStyle" and "PointStyle":
In[3]:= 

Out[3]= 

The options "PathStyle", "SpokeStyle", "CircleStyle" and "PointStyle" accept style directives:
In[4]:= 

Out[4]= 

All Graphics options are supported:
In[5]:= 

Out[5]= 

Explore loci of epicycles of radius 1/3, 1/2, 1:
In[6]:= 

Out[6]= 

This work is licensed under a Creative Commons Attribution 4.0 International License