Nodary

In physics and geometry, the nodary is the curve that is traced by the focus of a hyperbola as it rolls without slipping along the axis, a roulette curve.

The differential equation of the curve is: y 2 + 2 a y 1 + y ′ 2 = b 2 .

Its parametric equation is:

where k = cos ⁡ ( tan − 1 ⁡ ( b / a ) ) is the elliptic modulus and E ( u , k ) is the incomplete elliptic integral of the second kind and sn, cn and dn are Jacobi's elliptic functions.

The surface of revolution is the nodoid constant mean curvature surface.