Ellipse Rolling around Another Ellipse

base ellipse

eccentricity

0.75

rolling ellipse

semimajor axis

1.5

eccentricity

0.952

pole offset

0.

roll the ellipse

3.

This Demonstration draws the roulette of a generator point on an ellipse that rolls without slipping around a base ellipse.

Varying the semimajor axis or eccentricity of the rolling ellipse changes the circumference ratio

p

q

between the base ellipse and the rolling ellipse. A closed curve can be obtained after

q

complete revolutions around the base. By then the rolling 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.