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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2018-06-01
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| Series: | Results in Physics |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379718302262 |
| _version_ | 1818701600273727488 |
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| author | C. Mnasri A.A. Elmandouh |
| author_facet | C. Mnasri A.A. Elmandouh |
| author_sort | C. Mnasri |
| collection | DOAJ |
| 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 |
| first_indexed | 2024-12-17T15:23:25Z |
| format | Article |
| id | doaj.art-e3bafbbe00424e2ea5d7e4568fbfca59 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-17T15:23:25Z |
| publishDate | 2018-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-e3bafbbe00424e2ea5d7e4568fbfca592022-12-21T21:43:21ZengElsevierResults 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 |
| 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 |
| 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_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_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_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 |
| url | http://www.sciencedirect.com/science/article/pii/S2211379718302262 |
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