Equiform spacelike Smarandache curves of anti-eqiform Salkowski curve according to equiform frame

The concept of a pair of curves, called as Bertrand partner curves, was introduced by Bertrand in 1850. Bertrand partner curves have been studied widely in the literature from past to present. In this study, we take into account of the concept of Bertrand partner trajectories according to Positional Adapted Frame (PAF) for the particles moving in 3-dimensional Euclidean space. Some characterizations are given for these trajectories with the aid of the PAF elements. Then, we obtain some special cases of these trajectories. Moreover, we provide a numerical example.

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“…Then, α is an osculating curve if and only if k 1 = 0. More details can be found in the studies [11,15,16,19] for Positional Adapted Frame (PAF).…”

Section: Basic Conceptsmentioning

confidence: 99%

“…The authors defined this moving frame for the trajectories having non-vanishing angular momentum in Euclidean 3space [15]. There can be found some other studies [11,16,19] which are performed by considering this frame.…”

Section: Introductionmentioning

confidence: 99%

Bertrand partner P-trajectories in the Euclidean 3-space $E^3$

İşbilir

Özen

Tosun

2023

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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“…In this study, we investigated the Smarandache curves using the modified orthogonal frame to give a new perspective to curves. The Smarandache curves are characterized using different frames in Euclidean and non-Euclidean spaces [1][2][3][4][5][6][7][8][9]. The Smarandache curves obtained from spacelike Salkowski and anti-Salkowski curves are given by Eren and Şenyurt in Minkowski space [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

On Characterization of Smarandache Curves Constructed by Modified Orthogonal Frame

Eren,

Ersoy

2024

Mathematical Sciences and Applications E-Notes

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In this study, we investigate Smarandache curves constructed by a space curve with a modified orthogonal frame. Firstly, the relations between the Frenet frame and the modified orthogonal frame are summarized. Later, the Smarandache curves based on the modified orthogonal frame are obtained. Finally, the tangent, normal, binormal vectors and the curvatures of the Smarandache curves are determined. A special curve known as the Gerono lemniscate curve whose curvature is not differentiable, the principal normal and binormal vectors are discontinuous at zero point is considered as an example, and the Smarandache curves of this curve are obtained by the aid of its modified orthogonal frame, and their graphics are given.

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“…A geometry of Smarandache is a geometry that has at least one denied axiom Smarandachely (1969). Several researchers [5][6][7][8]11,14,[17][18][19][20]22] have recently studied Smarandache curves in Minkowski and the Euclidean spaces.…”

Section: Introductionmentioning

confidence: 99%