New Treatment of the Rotary Motion of a Rigid Body with Estimated Natural Frequency
In this paper, the problem of the motion of a rigid body about a fixed point under the action of a Newtonian force field is studied when the natural frequency ω=0.5. This case of singularity appears in the previous works and deals with different bodies which are classified according to the moments o...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Astronomy |
| Online Access: | http://dx.doi.org/10.1155/2020/6629183 |
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| author | A. I. Ismail |
| author_facet | A. I. Ismail |
| author_sort | A. I. Ismail |
| collection | DOAJ |
| description | In this paper, the problem of the motion of a rigid body about a fixed point under the action of a Newtonian force field is studied when the natural frequency ω=0.5. This case of singularity appears in the previous works and deals with different bodies which are classified according to the moments of inertia. Using the large parameter method, the periodic solutions for the equations of motion of this problem are obtained in terms of a large parameter, which will be defined later. The geometric interpretation of the considered motion will be given in terms of Euler’s angles. The numerical solutions for the system of equations of motion are obtained by one of the well-known numerical methods. The comparison between the obtained numerical solutions and analytical ones is carried out to show the errors between them and to prove the accuracy of both used techniques. In the end, we obtain the case of the regular precession type as a special case. The stability of the motion is considered by the phase diagram procedures. |
| format | Article |
| id | doaj-art-3c7d29f092204e3c91c51cdd1ce7c3a3 |
| institution | Kabale University |
| issn | 1687-7969 1687-7977 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Astronomy |
| spelling | doaj-art-3c7d29f092204e3c91c51cdd1ce7c3a32025-02-03T01:03:57ZengWileyAdvances in Astronomy1687-79691687-79772020-01-01202010.1155/2020/66291836629183New Treatment of the Rotary Motion of a Rigid Body with Estimated Natural FrequencyA. I. Ismail0Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, P.O. Box 5555, Makkah, Saudi ArabiaIn this paper, the problem of the motion of a rigid body about a fixed point under the action of a Newtonian force field is studied when the natural frequency ω=0.5. This case of singularity appears in the previous works and deals with different bodies which are classified according to the moments of inertia. Using the large parameter method, the periodic solutions for the equations of motion of this problem are obtained in terms of a large parameter, which will be defined later. The geometric interpretation of the considered motion will be given in terms of Euler’s angles. The numerical solutions for the system of equations of motion are obtained by one of the well-known numerical methods. The comparison between the obtained numerical solutions and analytical ones is carried out to show the errors between them and to prove the accuracy of both used techniques. In the end, we obtain the case of the regular precession type as a special case. The stability of the motion is considered by the phase diagram procedures.http://dx.doi.org/10.1155/2020/6629183 |
| spellingShingle | A. I. Ismail New Treatment of the Rotary Motion of a Rigid Body with Estimated Natural Frequency Advances in Astronomy |
| title | New Treatment of the Rotary Motion of a Rigid Body with Estimated Natural Frequency |
| title_full | New Treatment of the Rotary Motion of a Rigid Body with Estimated Natural Frequency |
| title_fullStr | New Treatment of the Rotary Motion of a Rigid Body with Estimated Natural Frequency |
| title_full_unstemmed | New Treatment of the Rotary Motion of a Rigid Body with Estimated Natural Frequency |
| title_short | New Treatment of the Rotary Motion of a Rigid Body with Estimated Natural Frequency |
| title_sort | new treatment of the rotary motion of a rigid body with estimated natural frequency |
| url | http://dx.doi.org/10.1155/2020/6629183 |
| work_keys_str_mv | AT aiismail newtreatmentoftherotarymotionofarigidbodywithestimatednaturalfrequency |