The Cochleoid

Introduction:

The cochleoid has an extremely simple parameterization, but complicated expressions for velocity, arclength, and curvature. The plot above is for the case n = 1 in the parameterization below, while the smaller plot below is the case n = 2.

Definition:

Properties:

Velocity and Acceleration:

a[t] = [click for formula]

 

The Tangent Vector:

Arc Length:

s[t] = [click for formula]

Curvature:

kappa[t] = [click for formula]