Associated curves of a Frenet curve and their applications

被引：51
|
作者：
Choi, Jin Ho [1 ]
Kim, Young Ho [1 ]
机构：
[1] Kyungpook Natl Univ, Dept Math, Taegu 702701, South Korea
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2012年 / 218卷 / 18期
基金：
新加坡国家研究基金会;
关键词：
Associated curve; Principal-direction curve; Principal-donor curve; General helix; Slant helix; PD-rectifying curve; Bertrand curve;
D O I：
10.1016/j.amc.2012.02.064
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce the notion of the principal (binormal)-direction curve and principal (binormal)-donor curve of a Frenet curve in E-3 and give the relationship of curvature and torsion of its mates. As application, we characterize general helices and slant helices in terms of their associated curves and give a canonical method to construct them. Also, we give a new characterization of Bertrand curve. Crown Copyright (C) 2012 Published by Elsevier Inc. All rights reserved.
引用
收藏
页码：9116 / 9124
页数：9
相关论文
共 50 条
  • [31] THE RELATION BETWEEN FRENET FRAME OF THE NATURAL LIFT CURVE AND BISHOP FRAME OF THE CURVE
    Ergun, Evren
    JOURNAL OF SCIENCE AND ARTS, 2021, (04): : 979 - 990
  • [32] The Frenet-Serret Framework for Aligning Geometric Curves
    Brunel, Nicolas J-B
    Park, Juhyun
    GEOMETRIC SCIENCE OF INFORMATION, 2019, 11712 : 608 - 617
  • [33] Construction of the Frenet-Serret frame of a curve in 4D Galilean space and some applications
    Yilmaz, Suha
    INTERNATIONAL JOURNAL OF THE PHYSICAL SCIENCES, 2010, 5 (08): : 1284 - 1289
  • [34] Generation of Optimum Frenet Curves by Genetic Algorithms for AGVs
    Bayona, Eduardo
    Sierra-Garc, J. Enrique
    Santos, Matilde
    ARTIFICIAL INTELLIGENCE APPLICATIONS AND INNOVATIONS, AIAI 2023, PT II, 2023, 676 : 454 - 464
  • [35] Curve matching on brain surfaces using frenet distances
    Bakircioglu, M
    Grenander, U
    Khaneja, N
    Miller, MI
    HUMAN BRAIN MAPPING, 1998, 6 (5-6) : 329 - 333
  • [36] Construction of a curve by using the state equation of Frenet formula
    Chen, J. T.
    Lee, J. W.
    Kao, S. K.
    Chou, Y. T.
    JOURNAL OF MECHANICS, 2021, 37 : 454 - 465
  • [37] ON THE NUMBER OF REAL CURVES ASSOCIATED TO A COMPLEX ALGEBRAIC CURVE
    BUJALANCE, E
    GROMADZKI, G
    SINGERMAN, D
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 120 (02) : 507 - 513
  • [38] Applications of the Frenet Frame to Electric Circuits
    Milano, Federico
    Tzounas, Georgios
    Dassios, Ioannis
    Kerci, Taulant
    IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2022, 69 (04) : 1668 - 1680
  • [39] DEFICIENCIES OF ASSOCIATED CURVES OF A HOLOMORPHIC CURVE IN PROJECTIVE SPACE
    NIINO, K
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 59 (01) : 81 - 88
  • [40] THE RELATION BETWEEN FRENET FRAME OF THE NATURAL LIFT CURVE AND BISHOP FRAME OF THE CURVE br
    Ergun, Evren
    JOURNAL OF SCIENCE AND ARTS, 2022, (04): : 979 - 990
12345