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NEW VERSION OF THE MAGNETIC CURVES ACCORDING TO THE BISHOP FRAME IN 𝔼<sup>3</sup>
Sariaydin, Muhammed T.,Korpinar, Talat The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.1
In this paper, it is investigated Lorentz force equations for $N_1$ and $N_2$-magnetic curves in 3-Dimensional Euclidean space. We give the Lorentz force in the Bishop frame in ${\mathbb{E}}^3$. Then, we obtain a new characterization for a magnetic field V. Also, we also give examples for each curve.
NEW VERSION OF THE MAGNETIC CURVES ACCORDING TO THE BISHOP FRAME IN E<sup>3</sup>
( Muhammed T. Sariaydin ),( Talat Korpinar ) 호남수학회 2019 호남수학학술지 Vol.41 No.1
In this paper, it is investigated Lorentz force equations for N<sub>1</sub> and N<sub>2</sub>-magnetic curves in 3-Dimensional Euclidean space. We give the Lorentz force in the Bishop frame in E<sup>3</sup>. Then, we obtain a new characterization for a magnetic field V . Also, we also give examples for each curve.
AN APPROACH FOR VECTORIAL MOMENTS IN EUCLIDEAN 3-SPACE
( Muhammed T. Sariaydin ),( Talat Körpinar ) 호남수학회 2020 호남수학학술지 Vol.42 No.1
In this paper, we investigate the vectorial moments of Bäcklund transformations of a space curve in E<sup>3</sup>. Firstly, it is obtained the vectorial moments which named αg dual curve, βg dual curve, and γg dual curve of Bäcklund transformations. Then we give the Euler elastic bending energies of these curves. Finally, we provide some examples of αg dual, βg dual, andγg dual, and their Euler elastic bending energies.
New version of the magnetic curves according to the Bishop frame in $\mathbb{E}^{3}$
Muhammed T. Sariaydin,Talat Korpinar 호남수학회 2019 호남수학학술지 Vol.41 No.1
In this paper, it is investigated Lorentz force equations for $N_{1}$ and $N_{2}$-magnetic curves in 3-Dimensional Euclidean space. We give the Lorentz force in the Bishop frame in $\mathbb{E}^{3}$. Then, we obtain a new characterization for a magnetic field $V$. Also, we also give examples for each curve.
Associated curves of charged particle moving with the effect of magnetic field
Muhammed Talat Sariaydin,Aziz Yazla 대한수학회 2023 대한수학회논문집 Vol.38 No.2
Magnetic curves are the trajectories of charged particals \linebreak which are influenced by magnetic fields and they satisfy the Lorentz equation. It is important to find relationships between magnetic curves and other special curves. This paper is a study of magnetic curves and this kind of relationships. We give the relationship between $\beta $-magnetic curves and Mannheim, Bertrand, involute-evolute curves and we give some geometric properties about them. Then, we study this subject for $\gamma $-magnetic curves. Finally, we give an evaluation of what we did.