Cycloid Consider one arch of the cycloid
as shown in the figure. Let be the arc length from the highest point on the arch to the point , and let be the radius of curvature at the point . Show that and are related by the equation . (This equation is called a natural equation for the curve.)
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CardioidsConsider the cardioids
as shown in the figure. Let be the arc length from the point on the cardioids to the point , and let be the radius of curvature at the point . Show that and are related by the equation . (This equation is called a natural equation for the curve.)
Curtate Cycloid A wheel of radius a rolls along a line without slipping. The curve traced by a point P that it b units front the center is called a curtate cycloid (see figure). Use the angle to find a set of parametric equations for this curve.
Curve CXcloid A wheel of radius rolls along a line without slipping.
The curve traced by a point P that it b units front the center (b< a) is called a curtate cycloid (see figure ).
Use the angle to find a set of parametric equations for this curve
Ā
