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

Its parametric equation is:

where ${\displaystyle k=\cos(\tan ^{-1}(b/a))}$ is the elliptic modulus and ${\displaystyle E(u,k)}$ is the incomplete elliptic integral of the second kind and sn, cn and dn are Jacobi's elliptic functions.

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