Evolution of curves via the velocities of the moving frame

Nassar H. Abdel-All, R. A. Hussien, Taha Youssef

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.



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How to Cite this Article:

Nassar H. Abdel-All, R. A. Hussien, Taha Youssef, Evolution of curves via the velocities of the moving frame, Journal of Mathematical and Computational Science, Vol 2, No 5 (2012), 1170-1185

Copyright © 2012 Nassar H. Abdel-All, R. A. Hussien, Taha Youssef. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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