Kinematic differential geometry of a rigid body in spatial motion using dual vector calculus: Part-I

In the present paper, the geometrical properties of a line trajectory in spatial motion are researched by using dual vector calculus. The invariants of a line trajectory generated by spatial motion are represented by that of the dual curve on the dual unit fixed sphere. Meanwhile the dual curvature...

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Bibliographic Details
Published in:Applied mathematics and computation 2006-12, Vol.183 (1), p.17-29
Main Author: Köse, Ö.
Format: Article
Language:English
Subjects:
Differential geometry
Dual points
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Geometry
Mathematics
Physics
Sciences and techniques of general use
Screw displacement
Solid dynamics (ballistics, collision, multibody system, stabilization...)
Solid mechanics
Spatial motion
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Summary:In the present paper, the geometrical properties of a line trajectory in spatial motion are researched by using dual vector calculus. The invariants of a line trajectory generated by spatial motion are represented by that of the dual curve on the dual unit fixed sphere. Meanwhile the dual curvature theories or the dual geodetic Euler–Savary analogue is set up. Some special cases of curvatures of a dual curve on the dual unit fixed sphere leads to the sets of lines with special kinematic meanings in the moving space. These lines will be discussed in the consecutive paper.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2006.02.054