Intrinsic Equations For A Relaxed Elastic Line Of Second Kind On An Oriented Surface
| Autor: | Emin Kasap, Ergin Bayram |
|---|---|
| Přispěvatelé: | Ondokuz Mayıs Üniversitesi |
| Rok vydání: | 2016 |
| Předmět: |
Mathematics - Differential Geometry
Surface (mathematics) Physics Physics and Astronomy (miscellaneous) Differential equation Computer Science::Information Retrieval calculus of variation 010102 general mathematics Mathematical analysis Astrophysics::Instrumentation and Methods for Astrophysics Torsion (mechanics) Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) 01 natural sciences 010101 applied mathematics Arc (geometry) Differential Geometry (math.DG) oriented surface Line (geometry) FOS: Mathematics Computer Science::General Literature Boundary value problem Calculus of variations 0101 mathematics Relaxed elastic line of second kind Arc length |
| Popis: | Let {\alpha}(s) be an arc on a connected oriented surface S in E3, parameterized by arc length s, with torsion {\tau} and length l. The total square torsion F of {\alpha} is defined by T=\int_{0}^{l}\tau ^{2}ds\ $. . The arc {\alpha} is called a relaxed elastic line of second kind if it is an extremal for the variational problem of minimizing the value of F within the family of all arcs of length l on S having the same initial point and initial direction as {\alpha}. In this study, we obtain differential equation and boundary conditions for a relaxed elastic line of second kind on an oriented surface. Comment: 8 pages |
| Databáze: | OpenAIRE |
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