Curve of Constant Precession

A curve whose centrode revolves about a fixed axis with constant angle and speed when the curve is traversed with unit speed. The tangent indicatrix of a curve of constant precession is a spherical helix. An arc length parameterization of a curve of constant precession with natural equations

			(1)
			(2)

is

			(3)
			(4)
			(5)

where

(6)

and , and are constant. This curve lies on a circular one-sheeted hyperboloid

(7)

The curve is closed iff is rational.