Circular Motion

Let's consider the following parametrized curve

x(t) = cos(a*t)
y(t) = sin(b*t)

These curves are called Lissajous curves after an 18th century physicist. They occur in models of oscillatory motion in two dimensions; for example, two coupled spring-mass systems.

Question #2

In Maple, plot Lissajous curves by varying a and b. Sketch the curves in your lab report and indicate the direction they were drawn.
- a := 1; b := -1;
- a := 3; b := 4;
- a := Pi; b := 4;
Hint: use the command
ParamPlot([cos(a*t), sin(b*t)], t = -Pi..Pi);
where you substitute in explicit values of a and b.
How does the last curve differ from the earlier ones? Use Maple commands like
plot([cos(Pi*t), sin(t), t= 0 ..100]);
to explore the long-term behavior of this curve. What will the curve look like as t approaches infinity?

Next: It's Like Riding a Bicycle
Up: Introduction
Previous: Parametrizing Planar Curves

Robert E. Thurman<thurman@geom.umn.edu>

Jeremy Case

Document Created: Mon Feb 20
Last modified: Tue Feb 27 08:51:21 1996