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- Title
三维欧氏空间中的特殊曲线.
- Authors
袁媛; 李静; 刘会立
- 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.
- Subjects
LOCUS (Mathematics); TORSION theory (Algebra); CENTER (Mathematics); CIRCLE; CURVES; VERTICAL circle
- Publication
Journal of Northeastern University (Natural Science), 2017, Vol 38, Issue 11, p1669
- ISSN
1005-3026
- Publication type
Article
- DOI
10.12068/j.issn.1005-3026.2017.11.030