东北大学学报（自然科学版）

东北大学学报:自然科学版 ›› 2017, Vol. 38 ›› Issue (11): 1669-1672.DOI: 10.12068/j.issn.1005-3026.2017.11.030

• 数学 • 上一篇    

三维欧氏空间中的特殊曲线

袁媛， 李静， 刘会立   

  1. (东北大学 理学院， 辽宁 沈阳110819)
  • 收稿日期:2015-06-15 修回日期:2015-06-15 出版日期:2017-11-15 发布日期:2017-11-13
  • 通讯作者: 袁媛
  • 作者简介:袁媛(1980- )，女，辽宁鞍山人，东北大学博士研究生; 刘会立(1959- )，男，辽宁辽阳人，东北大学教授，博士生导师.
  • 基金资助:
    教育部基本科研业务青年教师科研启动基金资助项目(N130305005).

Special Curves in 3-Dimensional Euclidean Space

YUAN Yuan， LI Jing， LIU Hui-li   

  1. School of Sciences， Northeastern University， Shenyang 110819， China.
  • Received:2015-06-15 Revised:2015-06-15 Online:2017-11-15 Published:2017-11-13
  • Contact: LIU Hui-li
  • About author:-
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摘要： 利用活动标架及曲线的理论与性质等研究了曲线的密切球中心轨迹以及从切平圆的性质. 首先，研究了曲线和曲线的密切球中心轨迹之间的关系， 并利用原曲线的曲率、挠率来确定曲线密切球中心轨迹的形状.当原曲线的曲率、挠率满足一定关系， 它的密切球中心轨迹分别是一般螺线、Bertrand曲线、Mannheim曲线对、从切曲线和球面曲线. 其次， 利用密切球面和从切平面的交线定义了从切圆并且研究了从切圆中心轨迹的性质.

关键词: 密切球中心轨迹, 从切圆, 曲率, 挠率, 从切曲线

Abstract: The properties of center locus of osculating sphere and the rectifying circle of curves were studied by using the theory and the properties of moving frame. First， the relationships between curves and the center locus of osculating sphere of curves were studied. Based on curvature and torsion， the figure of the center locus of osculating sphere of curves was obtained. And the center locus of osculating sphere of curves was generalized helix， Bertrand curves， Mannheim curves， rectifying curve and spherical curve， respectively， when curvature and torsion satisfied certain relation. Then， based on the intersection of osculating sphere and rectifying plane， the rectifying circles were obtained， and the properties of the center locus of rectifying circles were studied.

Key words: center trace of osculating sphere, rectifying circle, curvature, torsion, rectifying curve

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