A Novel Solution to the Frenet-Serret Equations

zbMATH Open1161.53003arXiv0709.2855MaRDI QIDQ3535036

Publication date: 10 November 2008

Abstract: A set of equations is developed to describe a curve in space given the curvature

k a p p a

and the angle of rotation

h e t a

of the osculating plane. The set of equations has a solution (in terms of

k a p p a

and

h e t a

) that indirectly solves the Frenet-Serret equations, with a unique value of

h e t a

for each specified value of

a u

. Explicit solutions can be generated for constant

h e t a

. The equations break down when the tangent vector aligns to one of the unit coordinate vectors, requiring a reorientation of the local coordinate system.

Full work available at URL: https://arxiv.org/abs/0709.2855

Mathematics Subject Classification ID

Curves in Euclidean and related spaces (53A04)

This page was built for publication: A Novel Solution to the Frenet-Serret Equations

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q3535036)