Заглавие | A MOTION OF A FAST SPINNING RIGID BODY ABOUT A FIXED POINT IN A SINGULAR CASE |
Вид публикация | Journal Article |
Година на публикуване | 1998 |
Автори | Ismail A |
Списание | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
Том | 90 |
Issue | Livre 2 - Mathématiques Appliquée et Informatique |
Pagination | 149-164 |
ISSN | 0205-0808 |
ключови думи | periodic solutions, rigid body motion, small parameter method |
Резюме | In this paper the problem of motion of a rigid body about a fixed point under the action of a Newtonian force field is studied for a singular value of the natural frequency ($\omega=1/3$). This singularity deals with different bodies being classified according to the moments of inertia. Using Poincaré's small parameter method, the periodic solutions - with non-zero basic amplitudes - of the quasi-linear autonomous system are obtained in the form of power series expansions, up to the third approximation, containing assumed small parameter. Also, the quasi-linear autonomous system is integrated numerically using any of the numerical integration methods, such as the fourth order Runge-Kutta method. At the end, a comparison between the analytical and the numerical solutions is given aiming to get a small deviation between them. |
1991/95 MSC | 70E05 |
Прикачен файл | Размер |
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90-149-164.pdf | 1.1 MB |