Evolution of curves via the velocities of the moving frame

Abstract

The purpose of the present work is to construct new geometrical models for the motion of plane and space curves using an approach different from the one proposed by R. Mukherjee and R. Balakrishnan [1]. This approach is applied to a pair of coupled nonlinear partial differential equations (CNLPDEs) governing the time evolution of the curvature and torsion of the evolving curve. For each model, solutions for CNLPDEs have been displayed by numerical integration of Frenet¡Seret equations.