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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.
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.