WOLFRAM|DEMONSTRATIONS PROJECT

Ellipse Rolling around a Circle

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ellipse eccentricity
0.85
generator offset
0
semimajor axis
1.279
roll the ellipse
3.5
This Demonstration draws a roulette of a generator point on an ellipse that rolls without slipping around a circle.
Varying the ellipse semimajor axis or eccentricity will change the circumference ratio
p
q
between the central circle and the ellipse. A closed curve can be obtained after
q
complete revolutions around the circle. By then the ellipse will have made
p+q
revolutions around its axis.
Changing the pole offset will further create a variety of curves. The bookmarks and snapshots give some examples.