##### Wikipedia

**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: $y^2 + \frac{2ay}{\sqrt{1+y'^2}}=b^2$.

Its parametric equation is:

$$x(u)=a\operatorname{sn}(u,k)+(a/k)\big((1-k^2)u - E(u,k)\big)$$

*y*(*u*) = − *a*cn(*u*, *k*) + (*a*/*k*)dn(*u*, *k*)

where *k* = cos(tan(*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.