Applying the Large Parameter Technique for Solving a Slow Rotary Motion of a Disc about a Fixed Point
In this paper, the motion of a disk about a fixed point under the influence of a Newtonian force field and gravity one is considered. We modify the large parameter technique which is achieved by giving the body a sufficiently small angular velocity component r0 about the fixed z-axis of the disk. Th...
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| Language: | English |
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Wiley
2020-01-01
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| Series: | International Journal of Aerospace Engineering |
| Online Access: | http://dx.doi.org/10.1155/2020/8854136 |
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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 motion of a disk about a fixed point under the influence of a Newtonian force field and gravity one is considered. We modify the large parameter technique which is achieved by giving the body a sufficiently small angular velocity component r0 about the fixed z-axis of the disk. The periodic solutions of motion are obtained in the neighborhood r0 tends to 0. This case of study is excluded from the previous works because of the appearance of a singular point in the denominator of the obtained solutions. Euler-Poison equations of motion are obtained with their first integrals. These equations are reduced to a quasilinear autonomous system of two degrees of freedom and one first integral. The periodic solutions for this system are obtained under the new initial conditions. Computerizing the obtained periodic solutions through a numerical technique for validation of results is done. Two types of analytical and numerical solutions in the new domain of the angular velocity are obtained. Geometric interpretations of motion are presented to show the orientation of the body at any instant of time t. |
| format | Article |
| id | doaj-art-2506384d53a54dc1bd4cc0c35a0cdddd |
| institution | OA Journals |
| issn | 1687-5966 1687-5974 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Aerospace Engineering |
| spelling | doaj-art-2506384d53a54dc1bd4cc0c35a0cdddd2025-08-20T02:04:30ZengWileyInternational Journal of Aerospace Engineering1687-59661687-59742020-01-01202010.1155/2020/88541368854136Applying the Large Parameter Technique for Solving a Slow Rotary Motion of a Disc about a Fixed PointA. I. Ismail0Department of Mechanics, College of Engineering and Islamic Architecture, Umm Al-Qura University, Makkah, P. O. Box 5555, Saudi ArabiaIn this paper, the motion of a disk about a fixed point under the influence of a Newtonian force field and gravity one is considered. We modify the large parameter technique which is achieved by giving the body a sufficiently small angular velocity component r0 about the fixed z-axis of the disk. The periodic solutions of motion are obtained in the neighborhood r0 tends to 0. This case of study is excluded from the previous works because of the appearance of a singular point in the denominator of the obtained solutions. Euler-Poison equations of motion are obtained with their first integrals. These equations are reduced to a quasilinear autonomous system of two degrees of freedom and one first integral. The periodic solutions for this system are obtained under the new initial conditions. Computerizing the obtained periodic solutions through a numerical technique for validation of results is done. Two types of analytical and numerical solutions in the new domain of the angular velocity are obtained. Geometric interpretations of motion are presented to show the orientation of the body at any instant of time t.http://dx.doi.org/10.1155/2020/8854136 |
| spellingShingle | A. I. Ismail Applying the Large Parameter Technique for Solving a Slow Rotary Motion of a Disc about a Fixed Point International Journal of Aerospace Engineering |
| title | Applying the Large Parameter Technique for Solving a Slow Rotary Motion of a Disc about a Fixed Point |
| title_full | Applying the Large Parameter Technique for Solving a Slow Rotary Motion of a Disc about a Fixed Point |
| title_fullStr | Applying the Large Parameter Technique for Solving a Slow Rotary Motion of a Disc about a Fixed Point |
| title_full_unstemmed | Applying the Large Parameter Technique for Solving a Slow Rotary Motion of a Disc about a Fixed Point |
| title_short | Applying the Large Parameter Technique for Solving a Slow Rotary Motion of a Disc about a Fixed Point |
| title_sort | applying the large parameter technique for solving a slow rotary motion of a disc about a fixed point |
| url | http://dx.doi.org/10.1155/2020/8854136 |
| work_keys_str_mv | AT aiismail applyingthelargeparametertechniqueforsolvingaslowrotarymotionofadiscaboutafixedpoint |