GEODESICS, LINE OF CURVATURES AND ASYMPTOTIC CURVES VERSUS RELAXED ELASTIC LINES ON AN ORIENTED SURFACE
JOURNAL OF SCIENCE AND ARTS, sa.1, ss.37-40, 2017 (ESCI)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2017
- Dergi Adı: JOURNAL OF SCIENCE AND ARTS
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
- Sayfa Sayıları: ss.37-40
- Anahtar Kelimeler: Relaxed elastic line, geodesic, line of curvature, asymptotic curve, INTRINSIC EQUATIONS, 3-SPACE
- Ondokuz Mayıs Üniversitesi Adresli: Evet
Özet
Let alpha(s) be an arc on a connected oriented surface S in E-3, parameterized by arc length s, with curvature k and length l. The total square curvature K of alpha is defined by K=integral(1)(0)kappa(2)The arc alpha is called a relaxed elastic line if it is an extremal for the variational problem of minimizing the value of K 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 show that a geodesic is a relaxed elastic line if and only if it is planar and an asymptotic curve cannot be a relaxed elastic line. Also, we obtain a criterion for a line of curvature to be a relaxed elastic line.