View source for Nodary

{{one source |date=May 2024}}
[[File:Nodary.svg|thumb|Nodary curve.]]
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]].<ref name="oprea">John Oprea, Differential Geometry and its Applications, MAA 2007. pp. 147–148</ref>

The differential equation of the curve is:
<math>y^2 + \frac{2ay}{\sqrt{1+y'^2}}=b^2</math>.

Its parametric equation is:
:<math>x(u)=a\operatorname{sn}(u,k)+(a/k)\big((1-k^2)u - E(u,k)\big)</math>
:<math>y(u)=-a\operatorname{cn}(u,k)+(a/k)\operatorname{dn}(u,k)</math>
where <math>k= \cos(\tan^{-1}(b/a))</math> is the elliptic modulus and <math>E(u,k)</math> is the [[incomplete elliptic integral of the second kind]] and sn, cn and dn are [[Jacobi's elliptic functions]].<ref name="oprea" />

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

==References==
{{reflist}}

[[Category:Plane curves]]


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