Results 101 to 110 of about 824,488 (198)

Serret-Frenet Formula of Quaternionic Framed Curves

Mathematical Sciences and Applications E-Notes
In this study, we present an approach by introducing the quaternionic structure of framed curves. Furthermore, we derive Serret-Frenet formulas and give specific results for quaternionic framed curves. Initially, we focus on the moving frame and its curvatures corresponding to the frame $ T,N,B $ along the quaternionic framed base curve in three ...
Zülal Derin Yaqub, Mehmet Ali Güngör
openaire   +2 more sources

Persistent Lorentzian Rigid Motions Generated by Slant Helices in Minkowski 3-Space

Mathematics
This paper develops a unified Lorentzian framework for persistent rigid motions generated by slant helices in three-dimensional Minkowski space and investigates their geometric and kinematic properties.
Derya Kahveci, Yusuf Yaylı
doaj   +1 more source

Modified Sweeping Surfaces in Euclidean 3-Space

Axioms
In this study, we explore the sweeping surfaces in Euclidean 3-space, utilizing the modified orthogonal frames with non-zero curvature and torsion, which allows us to consider the spine curves even if their second differentiations vanish.
Yanlin Li, Kemal Eren, Soley Ersoy, Ana Savić   +3 more
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Investigation of a curve using Frenet frame in the lightlike cone

Open Physics, 2017
Abstract Often times the language of mathematics is used to formulate physical theories. For example, as in this paper, while Minkowski space or the theory of special relativity were studying, their formulation was given by means of mathematical methods.
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PARALLEL TRANSPORTS WITH RESPECT TO FRENET AND DARBOUX FRAMES IN THE GALILEAN SPACE

, 2020
In this paper, we defined Fermi-Walker derivative in Galilean space G(3) Fermi-Walker transport and non-rotating frame by using Fermi-Walker derivative are given in G(3).
Sahin, Tevfik, Orbay, Keziban, Karakus, Fatma   +2 more
core  

Tracking the Frenet-Serret frame associated to a highly maneuvering target in 3D

, 2017
In this paper we consider the problem of tracking a maneuvering aircraft. The dynamical model used is based on assumptions of nearly constant tangential velocity, curvature, and torsion, of the target trajectory.
Pilté, Marion, Bonnabel, Silvère, Barbaresco, Frédéric   +2 more
core   +3 more sources

Inextensible Flow of Quaternionic Curves According to Type 2-Quaternionic Frame in the Euclidean Space [PDF]

In this paper, we investigate inextensible flows of quaternionic curve according to type 2-quaternionic frame. We give necessary and sufficient conditions for inextensible flow of quaternionic curves.
Yıldız, Önder Gökmen, Usta, Hazer
core   +1 more source

Slant Helices and Darboux Helices in Myller Configuration

Axioms
In this paper, we study slant helices (or ξ_2-helices) and Darboux helices in the Myller configuration M. We demonstrate that a curve in M is a slant helix if and only if it is a Darboux helix.
Yanlin Li, Akın Alkan, Mehmet Önder, Yuquan Xie   +3 more
doaj   +1 more source

A new frame for non-lightlike curves in Minkowski 3-space: hybrid frame

Demonstratio Mathematica
In this study, we introduce a hybrid frame consisting of elliptic, hyperbolic, and parabolic vectors for the study of non-lightlike curves in Minkowski 3-space.
Öztürk İskender, Çelik Oğuzhan, Çakır Hasan   +2 more
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Prediction-Error-Compensated Model Predictive Control with a Forgetting Factor for Ship Trajectory Tracking and Collision Avoidance

Journal of Marine Science and Engineering
To improve the prediction reliability of model predictive control under model mismatch and environmental disturbances, this paper proposes a prediction-error-compensated MPC method with a forgetting factor for ship trajectory tracking and collision ...
Wenxuan Ma, Xianku Zhang, Teer Guo
doaj   +1 more source