Three-dimensional Lissajous figures
Author
Manuel Rodrigues, Deyvid Pastana
Title
Three-dimensional Lissajous figures
Description
We show you how to represent several three-dimensional Lissajous figures in a table
Category
Working Material
Keywords
Three-dimensional Lissajous figures
URL
http://www.notebookarchive.org/2021-02-5ln0eis/
DOI
https://notebookarchive.org/2021-02-5ln0eis
Date Added
2021-02-12
Date Last Modified
2021-02-12
File Size
1.74 megabytes
Supplements
Rights
CC0 1.0
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Authors: Manuel E. Rodrigues and Deyvid W. da M. Pastana
Three-dimensional Lissajous figures
Three-dimensional Lissajous figures
Let’s start by clearing the memory from the file.
In[]:=
Quit[];
Lissajous figures can be obtained from the equations of motion of a restoring force in three dimensions, which represented graphically give us several possibilities of open or closed figures. We can have two general types of figures, the first class is obtained for the ratio between the oscillation frequencies is a rational number, then the motion is periodic. The second class is obtained when the ratio between the oscillation frequencies is an irrational number. In this notebook we will represent the periodic figures. We will start by defining the constants and the Cartesian coordinates.
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A=1;B=1;F=1;b=0;f=0;
In[]:=
x[t_,ωx_,ωy_,ωz_]:=A*Sin[ωx*t];y[t_,ωx_,ωy_,ωz_]:=B*Sin[ωy*t+b];z[t_,ωx_,ωy_,ωz_]:=F*Sin[ωz*t+f]
Now we define a generic point that depends on time and frequencies.
In[]:=
ponto[t_,ωx_,ωy_,ωz_]:={x[t,ωx,ωy,ωz],y[t,ωx,ωy,ωz],z[t,ωx,ωy,ωz]}
We can represent the figures by a parametric graph in three dimensions, as follows
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grafico[ωx_,ωy_,ωz_]:=ParametricPlot3D[ponto[t,ωx,ωy,ωz],{t,0,100},TicksNone,DisplayFunctionIdentity,PlotLabelStringJoin["ωx=",ToString[N[ωx]],"ωy=",ToString[N[ωy]],"ωz=",ToString[N[ωz]]],PlotStyleBlue,ImageSize90]
Finally, we create a table varying the chosen values for the frequencies, as follows
In[]:=
tabela=Table[Table[Table[grafico[ωx,ωy,ωz],{ωx,3,5,1}],{ωy,3,5,1}],{ωz,3,5,1}]
Out[]=
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Cite this as: Manuel Rodrigues, Deyvid Pastana, "Three-dimensional Lissajous figures" from the Notebook Archive (2021), https://notebookarchive.org/2021-02-5ln0eis
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