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2012-10-03T20:37:20Z

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[[File:Nodary.png|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>.
It has parametric equation
:<math>x(u)=a \mathrm{sn(u,k)}+(a/k)((1-k^2)u - E(u,k))</math>
:<math>y(u)=-\mathrm{cn(u,k)}+(a/k) \mathrm{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:Curves]]

Monoid factorisation - Revision history

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