A characterization of sliding vectors by dual numbers, some dual curves and the screw calculus

Abstract

Moving vectors, motors and screws are introduced and the mathematical background is explained: dual numbers are used for their description. Further, the paper deals with the dual space and curves in it. Some examples (in particular helices) are given. Newly, so called Spivak's dual curve is studied from the point of view of its natural parameterization; it is presented that curvature and torsion at zero are not able to distinguish this curve from the plane analogy again – as in the real case. It is also mentioned the applicability of the theory in mechanics.Moving vectors, motors and screws are introduced and the mathematical background is explained: dual numbers are used for their description. Further, the paper deals with the dual space and curves in it. Some examples (in particular helices) are given. Newly, so called Spivak's dual curve is studied from the point of view of its natural parameterization; it is presented that curvature and torsion at zero are not able to distinguish this curve from the plane analogy again – as in the real case. It is also mentioned the applicability of the theory in mechanics.