Sufficiently small rotations of Lagrange’s gyro
In this study, the motion of Lagrange’s gyro about its fixed point in the presence of a perturbed torque, a gyroscopic torque, and a varied restoring one is searched. We assume sufficiently small angular velocity components in the direction of the principal axes that differ from the dynamical symmet...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SAGE Publishing
2023-09-01
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| Series: | Journal of Low Frequency Noise, Vibration and Active Control |
| Online Access: | https://doi.org/10.1177/14613484231162447 |
| _version_ | 1797733333437775872 |
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| author | AI Ismail TS Amer WS Amer |
| author_facet | AI Ismail TS Amer WS Amer |
| author_sort | AI Ismail |
| collection | DOAJ |
| description | In this study, the motion of Lagrange’s gyro about its fixed point in the presence of a perturbed torque, a gyroscopic torque, and a varied restoring one is searched. We assume sufficiently small angular velocity components in the direction of the principal axes that differ from the dynamical symmetry one and a restoring torque that is considered to be greater than the perturbing one. In this manner, we replace the familiar small parameter that was used in previous works with a large one. In such cases, the gyro equations for motion (EOM) are formulated in the form of a two-degrees-of-freedom (DOF) autonomous system. We average the obtained system to get periodic solutions and motion’s geometric interpretation of the problem using the large parameter. The regular precession and the pure rotation of the motion are obtained. A numerical study is evaluated for asserted the used techniques and showed the influence of the changing parameters of motion on the gyro behavior. The trajectories of the motions and their stabilities are discussed and analyzed. The novelty of this work lies in how to adapt the method of large parameter (MLP) to solve the rigid body problem, especially since it has been assumed initially that its angular velocity or its initial energy are very small. MSC (2000): 70E20, 70E17, 70E15, 70E05 |
| first_indexed | 2024-03-12T12:27:40Z |
| format | Article |
| id | doaj.art-59d3ec5887664d859bcf0cc5bd97c4cb |
| institution | Directory Open Access Journal |
| issn | 1461-3484 2048-4046 |
| language | English |
| last_indexed | 2024-03-12T12:27:40Z |
| publishDate | 2023-09-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Journal of Low Frequency Noise, Vibration and Active Control |
| spelling | doaj.art-59d3ec5887664d859bcf0cc5bd97c4cb2023-08-29T19:37:22ZengSAGE PublishingJournal of Low Frequency Noise, Vibration and Active Control1461-34842048-40462023-09-014210.1177/14613484231162447Sufficiently small rotations of Lagrange’s gyroAI IsmailTS AmerWS AmerIn this study, the motion of Lagrange’s gyro about its fixed point in the presence of a perturbed torque, a gyroscopic torque, and a varied restoring one is searched. We assume sufficiently small angular velocity components in the direction of the principal axes that differ from the dynamical symmetry one and a restoring torque that is considered to be greater than the perturbing one. In this manner, we replace the familiar small parameter that was used in previous works with a large one. In such cases, the gyro equations for motion (EOM) are formulated in the form of a two-degrees-of-freedom (DOF) autonomous system. We average the obtained system to get periodic solutions and motion’s geometric interpretation of the problem using the large parameter. The regular precession and the pure rotation of the motion are obtained. A numerical study is evaluated for asserted the used techniques and showed the influence of the changing parameters of motion on the gyro behavior. The trajectories of the motions and their stabilities are discussed and analyzed. The novelty of this work lies in how to adapt the method of large parameter (MLP) to solve the rigid body problem, especially since it has been assumed initially that its angular velocity or its initial energy are very small. MSC (2000): 70E20, 70E17, 70E15, 70E05https://doi.org/10.1177/14613484231162447 |
| spellingShingle | AI Ismail TS Amer WS Amer Sufficiently small rotations of Lagrange’s gyro Journal of Low Frequency Noise, Vibration and Active Control |
| title | Sufficiently small rotations of Lagrange’s gyro |
| title_full | Sufficiently small rotations of Lagrange’s gyro |
| title_fullStr | Sufficiently small rotations of Lagrange’s gyro |
| title_full_unstemmed | Sufficiently small rotations of Lagrange’s gyro |
| title_short | Sufficiently small rotations of Lagrange’s gyro |
| title_sort | sufficiently small rotations of lagrange s gyro |
| url | https://doi.org/10.1177/14613484231162447 |
| work_keys_str_mv | AT aiismail sufficientlysmallrotationsoflagrangesgyro AT tsamer sufficientlysmallrotationsoflagrangesgyro AT wsamer sufficientlysmallrotationsoflagrangesgyro |