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Evolution of Generalized Space Curve as a Function of Its Local Geometry

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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.
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Abdel-All, N. , Mohamed, S. and Al-Dossary, M. (2014) Evolution of Generalized Space Curve as a Function of Its Local Geometry. Applied Mathematics, 5, 2381-2392. doi: 10.4236/am.2014.515230. 
 

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