Slant Helix Curves and Acceleration Centers

Slant Helix Curves and Acceleration Centers
Murat Bekar 1,∗ and Yusuf Yaylı 2
Necmettin Erbakan University, Department of Mathematics and Computer Sciences, Turkey
Ankara University, Department of Mathematics, Turkey
[email protected]
In the study, an alternative one-parameter motion to Frenet motion
of a rigid-body in 3-dimensional Euclidean space is given by moving the
coordinate frame N,C,W instead of the Frenet frame T,N,B along a unit
speed curve, where N, C and W correspond to, respectively, unit principal normal vector field, derivative vector field of the unit principal normal
vector field and Darboux vector field of the unit speed curve. Also the
concepts fixed axode, striction curve, instantaneous pole points, acceleration pole points (or acceleration centers) and instant screw axis (ISA) of
this alternative one-parameter motion are analyzed.
Keywords: C-Slant helix; Striction curve; Rigid-body motion; Acceleration center
Karatekin Mathematics Days 2014, C
¸ ankırı, TURKEY