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A New Approach to the Accretive Growth of Surfaces Via Hyperbolical Kinematics

Mathematical Methods in the Applied Sciences, Volume 48, Issue 16, Page 15349-15363, 15 November 2025.
ABSTRACT In the current work, we introduce the accretive growth of surfaces by using hyperbolical geometry. First, we describe hyperbolical kinematics along a generating curve to construct accretive surfaces having a hyperbolical cross‐section. The obtained surfaces are not only the ones having hyperbolical cross‐sections but also their material points
Gül Tuğ, Zehra Özdemir
wiley   +1 more source

Geometric Kinematic Approach to Rigid Objects with Point Contact Based on A Local-Surface Frame

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2018
Controlling the relative motion between two contactingrigid bodies is necessary when manipulation and locomotion tasks areencountered in robotics. In this paper, we express the kinematics ofspin-rolling motion of rigid objects with point contact based on
Vahide Bulut
doaj   +1 more source

Timelike tubes with Darboux frame in Minkowski 3-space

International Journal of Physical Sciences, 2013
In this study, we define a timelike tube around a spacelike curve with timelike binormal by taking Darboux frame instead of Frenet frame in Minkowski 3-space  QUOTE  . Subsequently, we compute the Gaussian curvature, the mean curvature, and the second Gaussian curvature of timelike tube with Darboux frame and obtained some characterizations for special
Kızıltuğ Sezai, Yaylı Yusuf
openaire   +2 more sources

Ruled Surfaces with Constant Slope Ruling According to Darboux Frame

Mathematical Sciences and Applications E-Notes, 2020
 The main scope of this paper is to examine ruled surfaces with constant slope ruling with respect to the given surface according to Darboux Frame. We give necessary and su¢ cient conditions for these types surfaces to be developable. Also, the investigations are observed under some special cases.
Ayşe YAVUZ, Fatma ATEŞ, Yusuf YAYLI
openaire   +3 more sources

A new version of energy and elastica for curves with extended darboux frame

Boletim da Sociedade Paranaense de Matemática, 2022
In this work, we research geometrical interpretation involved with the energy by ED-frame field of first and second kind on orientable hypersurface in E⁴. We explore the geometric properties of some graphics by way of energy. We apply totally diverse discussion and approach to illustrate bending energy functional for ED-frame field of first and second ...
Vedat Asil, Talat Körpınar, Yasin Ünlütürk   +2 more
openaire   +4 more sources

Characterization of imbricate-ruled surfaces via rotation-minimizing Darboux frame in Minkowski 3-space $ \mathrm{E}_1^3 $

AIMS Mathematics
Using a common tangent vector field to a surface along a curve, in this study we discussed a new Darboux frame that we referred to as the rotation-minimizing Darboux frame (RMDF) in Minkowski 3-space. The parametric equation resulting from the RMDF frame
Emad Solouma, Ibrahim Al-Dayel , Meraj Ali Khan, Youssef A. A. Lazer   +3 more
doaj   +1 more source

Galileo's ship and the relativity principle

Noûs, Volume 59, Issue 3, Page 585-611, September 2025.
Abstract It is widely acknowledged that the Galilean Relativity Principle, according to which the laws of classical systems are the same in all inertial frames in relative motion, has played an important role in the development of modern physics. It is also commonly believed that this principle holds the key to answering why, for example, we do not ...
Sebastián Murgueitio Ramírez
wiley   +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

Product of Exponentials (POE) Splines on Lie‐Groups: Limitations, Extensions, and Application to SO(3)$$ SO(3) $$ and SE(3)$$ SE(3) $$

International Journal for Numerical Methods in Engineering, Volume 126, Issue 14, 30 July 2025.
ABSTRACT Existing methods for constructing splines and Bézier curves on a Lie group G$$ G $$ involve repeated products of exponentials deduced from local geodesics, w.r.t. a Riemannian metric, or rely on general polynomials. Moreover, each of these local curves is supposed to start at the identity of G$$ G $$.
Andreas Müller
wiley   +1 more source

Characteristic properties of the ruled surface with Darboux frame in E^3

Kuwait Journal of Science, 2015
In this study, the ruled surface with Darboux frame is defined. Then, the ruled surfacescharacteristic properties which are related to the geodesic curvature, the normal curvature andthe geodesic torsion are investigated. The relation between the Darboux
GÜLSÜM YELİZ ŞENTÜRK, SALİM YÜCE
doaj