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Evolution of Generalized Space Curve as a Function of Its Local Geometry
Mathematics Department, Faculty of Science, Assiut University, Assiut, Egypt
Mathematics Department, Faculty of Science, Assiut University, Assiut, Egypt
Mathematics Department, Girls College of Science, University of Dammam, Dammam, KSA
- 1 Mathematics Department, Faculty of Science, Assiut University, Assiut, Egypt
- 2 Mathematics Department, Faculty of Science, Assiut University, Assiut, Egypt
- 3 Mathematics Department, Girls College of Science, University of Dammam, Dammam, KSA
Applied Mathematics·Volume 05 (2014)·Pages 2381–2392·Published 5 August 2014·DOI10.4236/am.2014.515230
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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 R 2 are given and plotted.
KeywordsInelastic CurveCurve FlowEvolution of Curves
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