Generating Lissajous Figures

Given two wheels connected by a belt and a point on the outer rim of each, one can generate a Lissajous figure by the motion of the wheels. The coordinates of a point on a wheel can be described by sine functions of a certain frequency and phase shift. The ratio of the radii at the ends of the belt determines the relative frequencies of the coordinate of the red point on the upper left wheel and the coordinate of the red point on the lower right wheel. If the starting position of a point on a wheel is offset by a certain angle, a phase shift occurs in the sine functions describing the coordinates of the point.
Drag either red point to move both wheels and the curve will be traced. You can change the radius of the axle on the lower right wheel and the offset angle between the starting positions of the points with the sliders. The radius controls the relative frequency of the and coordinates. When it is a rational number, a closed curve is generated; when it is irrational, the curve never closes and fills the square. The offset angle determines the phase shift of the coordinate of the red point of the upper left wheel and affects the shape of the Lissajous figure generated.



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+