The Motion of a Rigid Body with Irrational Natural Frequency
In this paper, we consider the problem of the rotational motion of a rigid body with an irrational value of the frequency ω. The equations of motion are derived and reduced to a quasilinear autonomous system. Such system is reduced to a generating one. We assume a large parameter μ proportional inve...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/8898733 |
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| author | A. I. Ismail |
| author_facet | A. I. Ismail |
| author_sort | A. I. Ismail |
| collection | DOAJ |
| description | In this paper, we consider the problem of the rotational motion of a rigid body with an irrational value of the frequency ω. The equations of motion are derived and reduced to a quasilinear autonomous system. Such system is reduced to a generating one. We assume a large parameter μ proportional inversely with a sufficiently small component ro of the angular velocity which is assumed around the major or the minor axis of the ellipsoid of inertia. Then, the large parameter technique is used to construct the periodic solutions for such cases. The geometric interpretation of the motion is obtained to describe the orientation of the body in terms of Euler’s angles. Using the digital fourth-order Runge-Kutta method, we determine the digital solutions of the obtained system. The phase diagram procedure is applied to study the stability of the attained solutions. A comparison between the considered numerical and analytical solutions is introduced to show the validity of the presented techniques and solutions. |
| format | Article |
| id | doaj-art-80609d185c7f42928adc13b5c7b76223 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-80609d185c7f42928adc13b5c7b762232025-02-03T01:00:18ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/88987338898733The Motion of a Rigid Body with Irrational Natural FrequencyA. I. Ismail0Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, Makkah, P. O. Box 5555, Saudi ArabiaIn this paper, we consider the problem of the rotational motion of a rigid body with an irrational value of the frequency ω. The equations of motion are derived and reduced to a quasilinear autonomous system. Such system is reduced to a generating one. We assume a large parameter μ proportional inversely with a sufficiently small component ro of the angular velocity which is assumed around the major or the minor axis of the ellipsoid of inertia. Then, the large parameter technique is used to construct the periodic solutions for such cases. The geometric interpretation of the motion is obtained to describe the orientation of the body in terms of Euler’s angles. Using the digital fourth-order Runge-Kutta method, we determine the digital solutions of the obtained system. The phase diagram procedure is applied to study the stability of the attained solutions. A comparison between the considered numerical and analytical solutions is introduced to show the validity of the presented techniques and solutions.http://dx.doi.org/10.1155/2020/8898733 |
| spellingShingle | A. I. Ismail The Motion of a Rigid Body with Irrational Natural Frequency Advances in Mathematical Physics |
| title | The Motion of a Rigid Body with Irrational Natural Frequency |
| title_full | The Motion of a Rigid Body with Irrational Natural Frequency |
| title_fullStr | The Motion of a Rigid Body with Irrational Natural Frequency |
| title_full_unstemmed | The Motion of a Rigid Body with Irrational Natural Frequency |
| title_short | The Motion of a Rigid Body with Irrational Natural Frequency |
| title_sort | motion of a rigid body with irrational natural frequency |
| url | http://dx.doi.org/10.1155/2020/8898733 |
| work_keys_str_mv | AT aiismail themotionofarigidbodywithirrationalnaturalfrequency AT aiismail motionofarigidbodywithirrationalnaturalfrequency |