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ENERGY ON A PARTICLE IN DYNAMICAL AND ELECTRODYNAMICAL FORCE FIELDS IN LIE GROUPS
( Talat Korpinar ),( Ridvan Cem Demirkol ) 호남수학회 2018 호남수학학술지 Vol.40 No.2
In this study, we firstly define equations of motion based on the traditional model Newtonian mechanics in terms of the Frenet frame adapted to the trajectory of the moving particle in Lie groups. Then, we compute energy on the moving particle in resultant force field by using geometrical description of the curva-ture and torsion of the trajectory belonging to the particle. We also investigate the relation between energy on the moving particle in different force fields and energy on the particle in Frenet vector fields.
A New Approach On The Curvature Dependent Energy For Elastic Curves in a Lie Group
Talat Korpinar,Ridvan Cem Demirkol 호남수학회 2017 호남수학학술지 Vol.39 No.4
Elastica is known as classical curve that is a solution of variational problem, which minimize a thin inextensible wire's bending energy. Studies on elastica has been conducted in Euclidean space firstly, then it has been extended to Riemannian manifold by giving different characterizations. In this paper, we focus on energy of the elastic curve in a Lie group. We attepmt to compute its energy by using geometric description of the curvature and the torsion of the trajectory of the elastic curve of the trajectory of the moving particle in the Lie group. Finally, we also investigate the relation between energy of the elastic curve and energy of the same curve in Frenet vector fields in the Lie group.
ENERGY ON A PARTICLE IN DYNAMICAL AND ELECTRODYNAMICAL FORCE FIELDS IN LIE GROUPS
Korpinar, Talat,Demirkol, Ridvan Cem The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.2
In this study, we firstly define equations of motion based on the traditional model Newtonian mechanics in terms of the Frenet frame adapted to the trajectory of the moving particle in Lie groups. Then, we compute energy on the moving particle in resultant force field by using geometrical description of the curvature and torsion of the trajectory belonging to the particle. We also investigate the relation between energy on the moving particle in different force fields and energy on the particle in Frenet vector fields.
On New Fermi Walker Derivative Of Biharmonic Particles In Heisenberg Spacetime
Talat Korpinar 호남수학회 2019 호남수학학술지 Vol.41 No.1
In practical applications play an new important role timelike biharmonic particle by Fermi-Walker derivative. In this article, we get a innovative interpretation about timelike biharmonic particle by means of Fermi-Walker derivative and parallelism in Heisenberg spacetime. With this new representation, we derive necessary and sufficient condition of the given particle to be the inextensible flow. Moreover, we provide several characterizations designed for this particles in Heisenberg spacetime.
A NEW CONSTRUCTION OF BIENERGY AND BIANGLE IN LORENTZ 5-SPACE
( Talat Korpinar ),( Yasin Unluturk ) 호남수학회 2021 호남수학학술지 Vol.43 No.1
In this study, we firstly compute the energies and the angles of Frenet vector fields in Lorentz 5-space L<sup>5</sup>. Then we obtain the bienergies and biangels of Frenet vector fields in L<sup>5</sup> by using the values of energies and angles. Finally, we present the relations among energies, angles, bienergies, and biangles with graphics.
ON NEW FERMI WALKER DERIVATIVE OF BIHARMONIC PARTICLES IN HEISENBERG SPACETIME
Korpinar, Talat The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.1
In practical applications play an new important role timelike biharmonic particle by Fermi-Walker derivative. In this article, we get a innovative interpretation about timelike biharmonic particle by means of Fermi-Walker derivative and parallelism in Heisenberg spacetime. With this new representation, we derive necessary and sufficient condition of the given particle to be the inextensible flow. Moreover, we provide several characterizations designed for this particles in Heisenberg spacetime.
A NEW APPROACH ON THE CURVATURE DEPENDENT ENERGY FOR ELASTIC CURVES IN A LIE GROUP
Korpinar, Talat,Demirkol, Ridvan Cem The Honam Mathematical Society 2017 호남수학학술지 Vol.39 No.4
Elastica is known as classical curve that is a solution of variational problem, which minimize a thin inextensible wire's bending energy. Studies on elastica has been conducted in Euclidean space firstly, then it has been extended to Riemannian manifold by giving different characterizations. In this paper, we focus on energy of the elastic curve in a Lie group. We attepmt to compute its energy by using geometric description of the curvature and the torsion of the trajectory of the elastic curve of the trajectory of the moving particle in the Lie group. Finally, we also investigate the relation between energy of the elastic curve and energy of the same curve in Frenet vector fields in the Lie group.
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.
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 $\mathbb{E}^{3}$
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.