Motion of Discrete Curves in the Plane

Abstract

Motion of discrete curves (piecewise linear curves) in the plane is discussed. A discrete analogue of the Frenet-Serret formula is presented. Compatibility of the discrete Frenet-Serret formula and the kinematical relation for the velocity yields a differential-difference equation for the “ curvature''. Relations between the discrete Frenet-Serret formula and the Ablowitz-Ladik scattering problem are shown.