On the dynamics aspects for the plane motion of a particle under the action of potential forces in the presence of a magnetic field

On the dynamics aspects for the plane motion of a particle under the action of potential forces in the presence of a magnetic field

This article deals with the general motion of a particle moving in the Euclidean plane under the influence of a conservative potential force in the presence of a magnetic field perpendicular to the plane of the motion. We introduce the conditions for which this motion is not algebraically integrable...

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Main Authors: C. Mnasri, A.A. Elmandouh
Format: Article
Language:English
Published: Elsevier 2018-06-01
Series:Results in Physics
Online Access:http://www.sciencedirect.com/science/article/pii/S2211379718302262
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spelling doaj-e3bafbbe00424e2ea5d7e4568fbfca592020-11-24T21:55:35ZengElsevierResults in Physics2211-37972018-06-019825831On the dynamics aspects for the plane motion of a particle under the action of potential forces in the presence of a magnetic fieldC. Mnasri0A.A. Elmandouh1Department of Mathematics and Statistics, College of Science, King Faisal University, P. O. Box 400, Al-Ahsaa 31982, Saudi Arabia; Corresponding author.Department of Mathematics and Statistics, College of Science, King Faisal University, P. O. Box 400, Al-Ahsaa 31982, Saudi Arabia; Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptThis article deals with the general motion of a particle moving in the Euclidean plane under the influence of a conservative potential force in the presence of a magnetic field perpendicular to the plane of the motion. We introduce the conditions for which this motion is not algebraically integrable by using Kowalevski’s exponents. We present the equilibrium positions and study their stability and moreover, we clarify that the existence of the magnetic field acts as a stabilizer for maximum unstable equilibrium points for the effective potential. We employ Lyapunov theorem to construct the periodic solutions near the equilibrium points. The allowed regions of motion are specified and illustrated graphically. Keywords: Non-integrability, Stability, Periodic solutionshttp://www.sciencedirect.com/science/article/pii/S2211379718302262
collection DOAJ
language English
format Article
sources DOAJ
author C. Mnasri
A.A. Elmandouh
spellingShingle C. Mnasri
A.A. Elmandouh
On the dynamics aspects for the plane motion of a particle under the action of potential forces in the presence of a magnetic field
Results in Physics
author_facet C. Mnasri
A.A. Elmandouh
author_sort C. Mnasri
title On the dynamics aspects for the plane motion of a particle under the action of potential forces in the presence of a magnetic field
title_short On the dynamics aspects for the plane motion of a particle under the action of potential forces in the presence of a magnetic field
title_full On the dynamics aspects for the plane motion of a particle under the action of potential forces in the presence of a magnetic field
title_fullStr On the dynamics aspects for the plane motion of a particle under the action of potential forces in the presence of a magnetic field
title_full_unstemmed On the dynamics aspects for the plane motion of a particle under the action of potential forces in the presence of a magnetic field
title_sort on the dynamics aspects for the plane motion of a particle under the action of potential forces in the presence of a magnetic field
publisher Elsevier
series Results in Physics
issn 2211-3797
publishDate 2018-06-01
description This article deals with the general motion of a particle moving in the Euclidean plane under the influence of a conservative potential force in the presence of a magnetic field perpendicular to the plane of the motion. We introduce the conditions for which this motion is not algebraically integrable by using Kowalevski’s exponents. We present the equilibrium positions and study their stability and moreover, we clarify that the existence of the magnetic field acts as a stabilizer for maximum unstable equilibrium points for the effective potential. We employ Lyapunov theorem to construct the periodic solutions near the equilibrium points. The allowed regions of motion are specified and illustrated graphically. Keywords: Non-integrability, Stability, Periodic solutions
url http://www.sciencedirect.com/science/article/pii/S2211379718302262
work_keys_str_mv AT cmnasri onthedynamicsaspectsfortheplanemotionofaparticleundertheactionofpotentialforcesinthepresenceofamagneticfield
AT aaelmandouh onthedynamicsaspectsfortheplanemotionofaparticleundertheactionofpotentialforcesinthepresenceofamagneticfield
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