Existential Properties of Algebraic Integrals of a Rigid Body
In this article, we consider kinematical considerations of a rigid body rotating around a given fixed point in a Newtonian force field exerted by an attractive center with a rotating couple about their principal axes of inertia. The kinematic equations and their well-known three elementary integrals...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Advances in Astronomy |
| Online Access: | http://dx.doi.org/10.1155/2022/9393658 |
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| author | A. I. Ismail W. S. Amer |
| author_facet | A. I. Ismail W. S. Amer |
| author_sort | A. I. Ismail |
| collection | DOAJ |
| description | In this article, we consider kinematical considerations of a rigid body rotating around a given fixed point in a Newtonian force field exerted by an attractive center with a rotating couple about their principal axes of inertia. The kinematic equations and their well-known three elementary integrals of the problem are introduced. The existence properties of the algebraic integrals are considered. Besides, we search as a special case of the fourth algebraic integral for the problem of the rigid body’s motion around a fixed point under the action of a Newtonian force field with an orbiting couple. Lagrange’s case and Kovalevskaya’s one are obtained. The large parameter is used for satisfying the existing conditions of the algebraic integrals. The comparison between the obtained results and the previous ones is arising. The numerical solutions of the regulating system of motion are obtained utilizing the fourth-order Runge-Kutta method and are plotted in some figures to illustrate the positive impact of the imposed forces and torques on the behavior of the body at any time. |
| format | Article |
| id | doaj-art-460971cfe0da48ad9931a2f13cc8eac3 |
| institution | Kabale University |
| issn | 1687-7977 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Astronomy |
| spelling | doaj-art-460971cfe0da48ad9931a2f13cc8eac32025-08-20T03:36:12ZengWileyAdvances in Astronomy1687-79772022-01-01202210.1155/2022/9393658Existential Properties of Algebraic Integrals of a Rigid BodyA. I. Ismail0W. S. Amer1Mechanical Engineering DepartmentDepartment of Mathematics and Computer ScienceIn this article, we consider kinematical considerations of a rigid body rotating around a given fixed point in a Newtonian force field exerted by an attractive center with a rotating couple about their principal axes of inertia. The kinematic equations and their well-known three elementary integrals of the problem are introduced. The existence properties of the algebraic integrals are considered. Besides, we search as a special case of the fourth algebraic integral for the problem of the rigid body’s motion around a fixed point under the action of a Newtonian force field with an orbiting couple. Lagrange’s case and Kovalevskaya’s one are obtained. The large parameter is used for satisfying the existing conditions of the algebraic integrals. The comparison between the obtained results and the previous ones is arising. The numerical solutions of the regulating system of motion are obtained utilizing the fourth-order Runge-Kutta method and are plotted in some figures to illustrate the positive impact of the imposed forces and torques on the behavior of the body at any time.http://dx.doi.org/10.1155/2022/9393658 |
| spellingShingle | A. I. Ismail W. S. Amer Existential Properties of Algebraic Integrals of a Rigid Body Advances in Astronomy |
| title | Existential Properties of Algebraic Integrals of a Rigid Body |
| title_full | Existential Properties of Algebraic Integrals of a Rigid Body |
| title_fullStr | Existential Properties of Algebraic Integrals of a Rigid Body |
| title_full_unstemmed | Existential Properties of Algebraic Integrals of a Rigid Body |
| title_short | Existential Properties of Algebraic Integrals of a Rigid Body |
| title_sort | existential properties of algebraic integrals of a rigid body |
| url | http://dx.doi.org/10.1155/2022/9393658 |
| work_keys_str_mv | AT aiismail existentialpropertiesofalgebraicintegralsofarigidbody AT wsamer existentialpropertiesofalgebraicintegralsofarigidbody |