The E. Study Maps of Circles on Dual Hyperbolic and Lorentzian Unit Spheres $H_{0}^{2}$ and $S_{1}^{2}$

Yaylı, Yusuf; Çalışkan, Abdussamet; Uğurlu, H. Hüseyin

doi:10.1353/mpr.2002.0013

Cited by 7 publications

(8 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Studies on Lorentzian space in recent years have taken an important place in the field of mathematical research. It can be seen as a part of differential geometry (see Yavuz & Erdogdu 5 and Yavuz & Yaylı 6 ) as well as robotics, computer graphics, most areas of physics, and kinematics (see Yaylı et al, 3 Kula & Yaylı, 7 and López 8 ). We mention some fundamental definitions and properties in Lorentzian space that we use in this paper.…”

Section: Basic Conceptsmentioning

confidence: 99%

See 2 more Smart Citations

Dual transformations and quaternions

Yüca

Yaylı

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

In this study, we are interested in the way quaternions to represent 3D and 4D rotations in Lorentzian space. We give a new method for obtaining a rotation matrix in Lorentzian space with the help of a unit quaternion. Furthermore, we prove that rotation matrices correspond to a quaternion leave invariant the same axis in Euclidean and Lorentzian space. Then, we introduce a semi‐orthogonal matrix representation of a quaternion curve in 4D space. Moreover, we provide applications and draw their figures to explore visual representations. Finally, due to the importance of the dual space in kinematics, robotics, and other areas related, we carry this work into their dual spaces by using a dual quaternion.

show abstract

Section: Basic Conceptsmentioning

confidence: 99%

“…The group SO(n) is a generalization of the rotation group SO (3) acting in R n . The group SO(3) in R 3 is related to the three-sphere S 3 .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dual transformations and quaternions

Yüca

Yaylı

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…timelike) ruled surface in R 3 1 . Therefore, we can say something about ruled surfaces in R 3 or R 3 1 when examining curves in D 3 or D 3 1 , respectively [9,[16][17][18].…”

Section: Introductionmentioning

confidence: 99%

“…18) and the principal directional curve of γ is a spacelike plane curve with spacelike principal normal in D 2 , (b) If |τ | κ = |m| < 1, then the position vector of γ is given by…”

mentioning

confidence: 99%

Associated curves of a Frenet curve in the dual Lorentzian space

ABALI¹,

Yücesan²

2022

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

View full text Add to dashboard Cite

In this work, we firstly introduce notions of principal directed curves and principal donor curves which are associated curves of a Frenet curve in the dual Lorentzian space D 3 1 . We give some relations between the curvature and the torsion of a dual principal directed curve and the curvature and the torsion of a dual principal donor curve. We show that the dual principal directed curve of a dual general helix is a plane curve and obtain the equation of dual general helix by using position vector of plane curve. Then we show that the principal donor curve of a circle in D 2 or a hyperbola in D 2 1 and the principal directed curve of a slant helix in D 3 1 are a helix and general helix, respectively. We explain with an example for the second case. Finally, according to causal character of the principal donor curve of principal directed rectifying curve in D 3 1 , we show this curve to correspond to any timelike or spacelike ruled surface in Minkowski 3−space R 3 1 .

show abstract

Hyper-dual matrices and dual transformations

Yüca

Yaylı

2022

Journal of Geometry and Physics

View full text Add to dashboard Cite

The E. Study Maps of Circles on Dual Hyperbolic and Lorentzian Unit Spheres $H_{0}^{2}$ and $S_{1}^{2}$

Cited by 7 publications

References 0 publications

Dual transformations and quaternions

Dual transformations and quaternions

Associated curves of a Frenet curve in the dual Lorentzian space

Hyper-dual matrices and dual transformations

Contact Info

Product

Resources

About