New Uniform Motion and Fermi–Walker Derivative of Normal Magnetic Biharmonic Particles in Heisenberg Space

Talat Körpinar,Mustafa Inc,Mehmet Ali Akinlar,Zeliha Körpinar,Yu-Ming Chu

doi:10.3390/sym12061017

Abstract

In the present paper, we firstly discuss the normal biharmonic magnetic particles in the Heisenberg space. We express new uniform motions and its properties in the Heisenberg space. Moreover, we obtain a new uniform motion of Fermi–Walker derivative of normal magnetic biharmonic particles in the Heisenberg space. Finally, we investigate uniformly accelerated motion (UAM), the unchanged direction motion (UDM), and the uniformly circular motion (UCM) of the moving normal magnetic biharmonic particles in Heisenberg space.

Highlights

In relativistic physics, mathematical description of the motion of the particle is given by its kinematics
The trajectories of uniformly accelerated motion (UAM) are shown as the prolongation on the space time of some integral curves of the new vector field defined on a convinced fiber bundle in the space time
Let α be a regular biharmonic particle and B be a magnetic field in Heisenberg space

Summary

Introduction

Mathematical description of the motion of the particle is given by its kinematics. The trajectories of UAM are shown as the prolongation on the space time of some integral curves of the new vector field defined on a convinced fiber bundle in the space time They found a new geometric approach to provide that an inextensible UAM viewer does not abandon in a limited appropriate time. This is genuine to presume that there could possibly be a few exterior forces impacting the tendencies of the particle including gravitational force, frictional force, normal force, etc By encouraged this point, we research new uniform motion of velocity magnetic biharmonic particles and some vector fields with Fermi–Walker derivative in Heisenberg space. Considering the Riemannian geometry and standard methods of differential geometry, we aim to investigate another significant magnetic trajectories on the 3D Riemannian manifold

The Heisenberg Group and Magnetic Particles

Uniform Motion for Normal Biharmonic Magnetic Particles

Conclusions