Elliptic Epitrochoid
Elliptic Epitrochoid
This Demonstration traces the path of a point (known as the pole or generator) fixed to an ellipse that rolls without slipping around a stationary base ellipse.
If the circumference ratio between the ellipses is the rational number, a closed curve is obtained after complete revolutions of the rolling ellipse around the base. By then the rolling ellipse will have made revolutions around its center.
p
q
q
p+q
In this Demonstration, the circumference ratios are either integers () or of the form (). Consequently, a curve closes after one or two revolutions of the rolling ellipse around the base ellipse.
q=1
p
2
q=2
Moving the pole inside or outside the rolling ellipse makes the elliptic epitrochoid either curtate or prolate.
Changing the eccentricity of either ellipse creates a great variety of curves.