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Original Articles
Special Bishop Motion and Bishop Darboux Rotation Axis of the Space Curve
Bahaddin Bukcubukcu@gop.edu.trGazi Osman Pasa University, Faculty of Sciences and Arts, Department of MathematicsTokat-TurkeyView full profile → , Murat Kemal Karacanmurat.karacan@usak.edu.trUsak University, Faculty of Sciences and Arts, Department of Mathematics1 Eylul Campus, 64200, Usak-TurkeyView full profile →
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- Published Online:
- 03 Jun 2013
- Article type:
- Original Articles
- Language:
- EN
- Article no.:
- 1726037X.2008.10698542
- Pages:
- 27–34
Abstract
A special Frenet motion with a one parameter has been given by Bottema [5] in E3. In this study, we have given a generalization of [5] to Bishop motion in Euclidean 3-space. Firstly, Bishop motion is defined for space curve α and then Darboux vector of this motion is calculated for fixed and moving spaces in E3.The Bishop darboux rotation for space curves in Euclidean space E3 is decomposed into two simultaneous rotations. The axes of these simultaneous rotations are joined by a simple mechanism. One of these axes is a parallel of the tangent vector of the curve, the direction of the other is the direction of the Bishop darboux vector of the curve. This decomposition of the Bishop darboux rotation yields a necessary condition for the curve to be closed.
Keywords
References
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