On Some Curves with Modified Orthogonal Frame in Euclidean 3-Space

Lone, Mohamd Saleem; Es, Hasan; Karacan, Murat Kemal; Bükcü, Bahaddin

doi:10.1007/s40995-018-0661-2

Cited by 21 publications

(11 citation statements)

References 11 publications

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“…Later, Lone et al have studied helices and the Bertrand curves according to modified orthogonal frame in the Euclidean 3-space. They have investigated some theorems and results concerning this frame and given examples [16]. The paper is arranged as follows.…”

Section: Introductionmentioning

confidence: 99%

Involute-Evolute Curves According to Modified Orthogonal Frame

Azak

2021

J. Sci. Arts

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In this paper, the involute-evolute curve concept has been deﬁned according to two type modiﬁed orthogonal frames at non-zero points of curvature and torsion in the Euclidean space E^3 , respectively. Later, the characteristic theorems related to the distance between the corresponding points of these curves have been given. Besides, the relations have been found between the curvatures and also torsions of the two type the involute-evolute modiﬁed orthogonal pairs.

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Section: Introductionmentioning

confidence: 99%

Involute-Evolute Curves According to Modified Orthogonal Frame

Azak

2021

J. Sci. Arts

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“…There is a very close relation between this frame and Serret-Frenet frame. In the literature, there have been numerous studies about the Modified orthogonal frame [11,12,13,14,15]. In this paper, firstly, we have given a short knowledge about the Serret-Frenet frame and modified orthogonal frame.…”

Section: Introductionmentioning

confidence: 99%

A Note on the Acceleration and Jerk in Motion Along a Space Curve

Özen¹,

Güner

Tosun

2020

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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The resolution of the acceleration vector of a particle moving along a space curve is well known thanks to Siacci [1]. This resolution comprises two special oblique components which lie in the osculating plane of the curve. The jerk is the time derivative of acceleration vector. For the jerk vector of the aforementioned particle, a similar resolution is presented as a new contribution to field [2]. It comprises three special oblique components which lie in the osculating and rectifying planes. In this paper, we have studied the Siacci’s resolution of the acceleration vector and aforementioned resolution of the jerk vector for the space curves which are equipped with the modified orthogonal frame. Moreover, we have given some illustrative examples to show how the our theorems work.

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“…Moreover Bukcu and Karacan studied space curves and spherical curves with respect to the modified orthogonal frame in Minkowski and Euclidean space [2,3]. Recently, Lone et al obtained some characterization results for helices, Bertrand curves and Mannheim curves with respect to the modified orthogonal frame [7,8]. Considering all these studies, the idea of constructing the adjoint curve of a curve according to the modified orthogonal frame formed by torsion was born in this study.…”

Section: Introductionmentioning

confidence: 99%