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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.
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