Fourth-order kinematic analysis: Advanced decomposition methods for particle motion in modified orthogonal frame. [PDF]
PLoS ONEThe analysis of higher-order derivatives of position, particularly the snap (fourth derivative), provides critical insights into complex motion dynamics in fields such as robotics, aerospace, and biomechanics.
Fatimah Alghamdi, Ayman Elsharkawy
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Ruled Surfaces of Adjoint Curve with the Modified Orthogonal Frame
Journal of New TheoryThis paper analyzes several specific ruled surfaces generated by the base curve $\alpha$ and its director curve or the $\alpha$'s adjoint curve $\beta$ and its director curve, where the director curves are frame vectors of the modified orthogonal frame ...
Nural Yüksel +3 more
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Ruled Surfaces and Their Geometric Invariants via the Orthogonal Modified Frame in Minkowski 3-Space
MathematicsRuled surfaces in Minkowski 3-space play a crucial role in differential geometry and have significant applications in physics and engineering. This study explores the fundamental properties of ruled surfaces via orthogonal modified frame in Minkowski ...
Emad Solouma +2 more
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AxiomsIn this paper, we investigate the problem of designing surface pencil pairs through Bertrand curves as iso-curvature lines in three-dimensional Euclidean space.
Haytham A. Ali, Awatif Al-Jedani
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On the Characterisations of Curves with Modified Orthogonal Frame in $\mathbb{E}^{3}$
Journal of New Theory, 2022 This study analyses (k,m)-type slant helices in compliance with the modified orthogonal frame in 3-dimensional Euclidean space ($\mathbb{E}^{3}$). Furthermore, we perform some characterisations of curves with modified orthogonal frames in $\mathbb{E}^{3}$
Mehmet Bektaş, Şeyda Özel
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On the characterizations of special adjoint curves and surface family for the modified orthogonal frame with torsion [PDF]
Mathematica BohemicaIn this context, the main interest of this paper is to construct a family of surfaces in $E^3$ space which is the adjoint pair of a given curve. Then, using the modified orthogonal frame with torsion, we express the necessary conditions for the surface ...
Gülnur Şaffak Atalay
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Salkowski Curves and Their Modified Orthogonal Frames in $\mathbb{E}^{3}$
Journal of New Theory, 2022 In this study, we examine some properties of Salkowski curves in $\mathbb{E}^{3}$. We then make sense of the angle $(nt)$ in the parametric equation of the Salkowski curves.
Mehmet Bektaş +2 more
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Characterization of k,m-Type Slant Helices Using the Modified Orthogonal Frame in Minkowski 3-Space
Journal of MathematicsWithin the scope of differential geometry, exploring how curves relate to each other has long been a broad area of study for many scholars. When investigating curves, particularly space curves, the concept of frame fields, such as the Frenet–Serret frame,
Md Ajmal Khan +4 more
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Tzitzeica Curves According to Modified Orthogonal Frames
Cumhuriyet Science JournalThis paper explores Tzitzeica curves in three-dimensional Euclidean space through the use of modified orthogonal frames constructed via curvature and torsion functions.
Esra Damar
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AW(k)-Type Curves in Modified Orthogonal Frame
Türk Doğa Ve Fen DergisiThe goal of this article is to examine AW(k)-type curves in Euclidean 3- space according to a modified orthogonal frame with the non-zero curvature. Firstly, the relations between the curvatures for AW(k)-type curves in modified orthogonal frame are ...
Burçin Saltık +2 more
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