WOLFRAM|DEMONSTRATIONS PROJECT

Ellipse Rolling inside a Circle

​
ellipse eccentricity
0.821
generator offset
0.
semimajor axis
0.5
roll the ellipse
9.5
This Demonstration draws the roulette of a generator point on an ellipse that rolls without slipping inside a circle.
Varying the ellipse's semimajor axis or eccentricity changes the circumference ratio
p
q
between the circle and the ellipse. A closed curve can be obtained after
q
complete revolutions inside the circle. By then, the ellipse will have made
p-q
revolutions around its center.
Change the pole offset to create an even greater variety of curves. The bookmarks and snapshots give some examples.