Results 81 to 90 of about 824,488 (198)

ON GENERALIZED FRAMED AND FRENET-TYPE FRAMED BERTRAND CURVES IN EUCLIDEAN 3-SPACE

Facta Universitatis, Series: Mathematics and Informatics
In this paper, we consider Framed and Frenet-type Framed Bertrand curves. We generalized the notion of Framed and Frenet-type Framed Bertrand curves in Euclidean 3-space. According to this generalization, the Bertrand curve conditions of a given Framed and Frenet-type Framed Bertrand curves are obtained and the relations between the moving frames and ...
Hatice Altın Erdem, Bilge Guldu, Kazım Erdem   +2 more
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Smarandache Curves of Mannheim Curve Couple According to Frenet Frame

Mathematical Sciences and Applications E-Notes, 2017
p>In this paper, when the unit Darboux vector of the partner curve of Mannheimnbsp;curve are taken as the position vectors, the curvature and the torsion of Smarandache curvenbsp;are calculated. These values are expressed depending upon the Mannheim curve. Besides,nbsp;we illustrate example of our main results./p>
ŞENYURT, Süleyman, ÇALIŞKAN, Abdussamet   +1 more
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Efficient Trajectory Planning for Obstacle Avoidance in the Frenet Space based on High-Definition Map

, 2021
With the high-definition (HD) maps, we propose an efficient cost-based trajectory planning algorithm in the Frenet frame. Our effective ´ representation of obstacles and structured roads in the Frenet space allows faster ´ path generation and selection ...
Myung, Hyun, Jung, Euigon
core   +1 more source

Exploring Minimal Surfaces in E3: A Frenet-Like Curve (Flc) Approach and Differential Characterizations

Journal of Mathematics
This research article presents minimal surfaces in the Euclidean 3−space according to the Frenet-like curve frame (Flc-frame). The proposed methodology involves studying the necessary and sufficient conditions for a surface Ms,t to be a minimal surface ...
Safaa Mosa, Eman Ghareeb Rezk, Mervat Elzawy   +2 more
doaj   +1 more source

MOTION OF CURVES USING QUASI FRAME [PDF]

Assiut University Journal of Multidisciplinary Scientific Research, 2018
In this paper, evolution of space curves using quasi frame are considered. We derive a pair of coupled partialdifferential equations that governing the time evolution for the quasi curvatures of the evolving curve.
doaj   +1 more source

Exploration of the Character Representation of DNA Chiral Conformations and Deformations via a Curved Surface Discrete Frenet Frame. [PDF]

Int J Mol Sci, 2023
Wang Y, Wang H, Zhang S, Yang Z, Shi X, Zhang L.   +5 more
europepmc   +1 more source

Frenet frame

, 2014
This educational Demonstration, primarily for vector calculus students, shows the moving Frenet frame (or TNB frame, for tangent, normal, and binormal).
Bykov, Nick
core  

A New Approach on Helices in Pseudo-Riemannian Manifolds

Abstract and Applied Analysis, 2014
A proper curve α in the n-dimensional pseudo-Riemannian manifold (M,g) is called a Vn-slant helix if the function g(Vn,X) is a nonzero constant along α, where X is a  parallel vector field along α and Vn is nth Frenet frame.
Evren Zıplar, Yusuf Yaylı, İsmail Gök   +2 more
doaj   +1 more source

Frenet formulas and . . . [PDF]

, 2007
In this paper we deal with one of the homogeneous 3-geometries, the Sol geometry. The Frenet frame and the curvature and torsion of a curve has been determined, moreover, we have computed the parametric form of geodesics, their curvatures and torsions in
Brigitta Szilágyi, Attila Bölcskei
core  

Bi-Hamiltonian Structure in Serret-Frenet Frame

, 2007
We reduced the problem of constructing bi-Hamiltonian structure in three dimensions to the solution of a Riccati equation in moving coordinates of Serret-Frenet frame. We then show that either the linearly independent solutions of the corresponding second order equation or the normal vectors of the moving frame imply two compatible Poisson structures.
Abadoglu, E., Gumral, H.
openaire   +2 more sources