Rotating strings

TL;DR

This paper derives analytical solutions for the configurations of a rotating inextensible, flexible string, including helices and non-helical curves, governed by a cubic equation, with only coplanar curves touching the axis.

Contribution

It provides explicit analytical expressions for the shapes of a rotating string, expanding understanding of its possible configurations and the governing equations.

Findings

Helical solutions with arbitrary radius and pitch are identified.

Non-helical solutions are characterized by roots of a cubic equation.

Only coplanar curves with the axis can contact it.

Abstract

Analytical expressions are provided for the configurations of an inextensible, flexible, twistable inertial string rotating rigidly about a fixed axis. Solutions with trivial radial dependence are helices of arbitrary radius and pitch. Non-helical solutions are governed by a cubic equation whose roots delimit permissible values of the squared radial coordinate. Only curves coplanar with the axis of rotation make contact with it.