TITLE:
Evolution of Generalized Space Curve as a Function of Its Local Geometry
AUTHORS:
Nassar H. Abdel-All, Samah G. Mohamed, Mariam T. Al-Dossary
KEYWORDS:
Inelastic Curve, Curve Flow, Evolution of Curves
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.15,
August
19,
2014
ABSTRACT: Kinematics of
moving generalized curves in a n-dimensional Euclidean space is formulated in
terms of intrinsic geometries. The evolution equations of the orthonormal frame
and higher curvatures are obtained. The integrability conditions for the
evolutions are given. Finally, applications in R2 are
given and plotted.