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. [1]

Nodary curve.

The differential equation of the curve is: .

Its parametric equation is:

where is the elliptic modulus and is the incomplete elliptic integral of the second kind and sn, cn and dn are Jacobi's elliptic functions.[1]

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

References

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  1. ^ a b John Oprea, Differential Geometry and its Applications, MAA 2007. pp. 147–148