JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A STUDY ON A RULED SURFACE WITH LIGHTLIKE RULING FOR A NULL CURVE WITH CARTAN FRAME
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
A STUDY ON A RULED SURFACE WITH LIGHTLIKE RULING FOR A NULL CURVE WITH CARTAN FRAME
Ayyildiz, Nihat; Turhan, Tunahan;
  PDF(new window)
 Abstract
In this study, we investigate the curvature functions of ruled surface with lightlike ruling for a null curve with Cartan frame in Minkowski 3-space. Also, we give relations between the curvature functions of this ruled surface and curvature functions of central normal surface. Finally, we use the curvature theory of the ruled surface for determine differential properties of a robot end-effector motion.
 Keywords
rigid body;null scroll;Cartan frame;Frenet formulae;striction curve;
 Language
English
 Cited by
 References
1.
L. J. Alias, A. Ferrandez, P. Lucas, and M. A. Moreno, On the Gauss map of Bscrolls, Tsukuba J. Math. 22 (1998), no. 2, 371-377.

2.
N. Ayylldlz and A. Yucesan, On the scalar and dual formulations of the curvature theory of line trajectories in the Lorentzian space, J. Korean Math. Soc. 43 (2006), no. 6, 1339-1355. crossref(new window)

3.
H. Balgetir, M. Bektas, and M. Ergut, Null scroll in the 3-dimensional Lorentzian space, Appl. Sci. 5 (2003), no. 1, 1-5.

4.
W. B. Bonnor, Null hypersurfaces in Minkowski space-time, Tensor (N. S.) 24 (1972), 329-345.

5.
S. M. Choi, U. H. Ki, and Y. J. Suh, On the Gauss map of null scrolls, Tsukuba J. Math. 22 (1998), no. 1, 273-279. crossref(new window)

6.
A. C. Coken and U. Ciftci, On null curves on surfaces and null vectors in Lorentz space, SDU Fen Derg. 2 (2007), no. 1, 111-116.

7.
K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Academic Publishers, 1996.

8.
S. Ersoy and M. Tosun, On the trajectory null scrolls in 3-dimensional Minkowski spacetime E3 1 , Kyungpook Math. J. 48 (2008), no. 1, 81-92. crossref(new window)

9.
A. Ferrandez and P. Lucas, On surfaces in the 3-dimensional Lorentz-Minkowski space, Pacific J. Math. 152 (1992), no. 1, 93-100. crossref(new window)

10.
A. Ferrandez, A. Gimenez, and P. Lucas, Null helices in Lorentzian space forms, Internat. J. Modern Phys. A. 16 (2001), no. 30, 4845-4863. crossref(new window)

11.
H. Liu, Ruled surfaces with lightlike ruling in 3-Minkowski space, J. Geom. Phys. 59 (2009), no. 1, 74-78. crossref(new window)

12.
J. M. McCarthy, On the scalar and dual formulations of the curvature theory of line trajectories, Journal of Mechanisms, Transmissions, and Automation in Design 109 (1987), 101-106. crossref(new window)

13.
J. M. McCarthy and B. Roth, The curvature theory of line trajectories in spatial kine- matics, ASME Journal of Mechanical Design 103 (1981), no. 4, 718-724. crossref(new window)

14.
B. S. Ryuh, Robot trajectory planning using the curvature theory of ruled surfaces, Doctoral dissertation, Purdue University, West Lafayette, Ind, USA, 1989.