The Stability of Certain Motion of a Charged Gyrostat in Newtonian Force Field
This work aims to study the stability of certain motions of a rigid body rotating about its fixed point and carrying a rotor that rotates with constant angular velocity about an axis parallel to one of the principal axes. This motion is presumed to take place due to the combined influence of the mag...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Advances in Astronomy |
| Online Access: | http://dx.doi.org/10.1155/2021/6660028 |
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| author | A. A. Elmandouh Fatimah H. Alsaad |
| author_facet | A. A. Elmandouh Fatimah H. Alsaad |
| author_sort | A. A. Elmandouh |
| collection | DOAJ |
| description | This work aims to study the stability of certain motions of a rigid body rotating about its fixed point and carrying a rotor that rotates with constant angular velocity about an axis parallel to one of the principal axes. This motion is presumed to take place due to the combined influence of the magnetic field and the Newtonian force field. The equations of motion are deduced, and moreover, they are expressed as a Lie–Poisson Hamilton system. The permanent rotations are calculated and interpreted mechanically. The sufficient conditions for instability are presented employing the linear approximation method. The energy-Casimir method is applied to gain sufficient conditions for stability. The regions of linear stability and Lyapunov stability are illustrated graphically for certain values of the parameters. |
| format | Article |
| id | doaj-art-0f7a180a414444b4a55fc05f1b2ebd3a |
| institution | Kabale University |
| issn | 1687-7969 1687-7977 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Astronomy |
| spelling | doaj-art-0f7a180a414444b4a55fc05f1b2ebd3a2025-02-03T01:05:07ZengWileyAdvances in Astronomy1687-79691687-79772021-01-01202110.1155/2021/66600286660028The Stability of Certain Motion of a Charged Gyrostat in Newtonian Force FieldA. A. Elmandouh0Fatimah H. Alsaad1Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsaa 31982, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsaa 31982, Saudi ArabiaThis work aims to study the stability of certain motions of a rigid body rotating about its fixed point and carrying a rotor that rotates with constant angular velocity about an axis parallel to one of the principal axes. This motion is presumed to take place due to the combined influence of the magnetic field and the Newtonian force field. The equations of motion are deduced, and moreover, they are expressed as a Lie–Poisson Hamilton system. The permanent rotations are calculated and interpreted mechanically. The sufficient conditions for instability are presented employing the linear approximation method. The energy-Casimir method is applied to gain sufficient conditions for stability. The regions of linear stability and Lyapunov stability are illustrated graphically for certain values of the parameters.http://dx.doi.org/10.1155/2021/6660028 |
| spellingShingle | A. A. Elmandouh Fatimah H. Alsaad The Stability of Certain Motion of a Charged Gyrostat in Newtonian Force Field Advances in Astronomy |
| title | The Stability of Certain Motion of a Charged Gyrostat in Newtonian Force Field |
| title_full | The Stability of Certain Motion of a Charged Gyrostat in Newtonian Force Field |
| title_fullStr | The Stability of Certain Motion of a Charged Gyrostat in Newtonian Force Field |
| title_full_unstemmed | The Stability of Certain Motion of a Charged Gyrostat in Newtonian Force Field |
| title_short | The Stability of Certain Motion of a Charged Gyrostat in Newtonian Force Field |
| title_sort | stability of certain motion of a charged gyrostat in newtonian force field |
| url | http://dx.doi.org/10.1155/2021/6660028 |
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