Secular perturbations of the translational-rotational motion in the problem of the two non-stationary bodies: sphere - axisymmetric body

  • M. Zh. Minglibayev Астрофизический институт им. В.Г. Фесенкова, Алматы, Казахстан
  • O. B. Baisbayeva Казахский Национальный Университет имени аль-Фараби

Abstract

In this article we consider mutually gravitating non-stationary two bodies: first body is "central it is a sphere with a spherical density distribution, the second body is "satellite which has an axisymmetric dynamic structure and form. Newtonian force interaction is characterized by an approximate expression of the force function, which takes into account the second harmonic. Masses of bodies change isotropic in the different rates. Equations of the perturbed translational-rotational motion of satellite are deduced in the new osculating elements. Full secular perturbations of translational-rotational motion of non-stationary axisymmetric body for arbitrary laws of variation of masses and sizes are obtained. As a result, it is possible to study the translational-rotational motion of the axisymmetric body in two cases of nonstationary: the first case - the variation of the size of the axisymmetric body with variable mass is homothetic and shape remains unchanged, the second case is non-stationary axisymmetric body characterized by variable size, variable masses and variable oblate.

References

[1] Минглибаев М.Дж. Динамика нестационарных гравитирующих систем. - Алматы:Изд. «Қазақ университетi», 2009. - 209 с.

[2] Минглибаев М.Дж. К канонической теории возмущений в небесной механике телпеременной массы // Труды АФИ АН Каз ССР. - 1992. - Т. 50. - С. 71-78.

[3] Минглибаев М.Дж. К вращательному движению нестационарного тела // Известия МОН РК, серия физико-математическая. - 2006. - №4. - С. 10-13.

[4] Белецкий В.В. Движение спутника относительно центра масс в гравитационном поле. - Москва: МГУ им. М.В. Ломоносова, 1975. - 308 с.
How to Cite
MINGLIBAYEV, M. Zh.; BAISBAYEVA, O. B.. Secular perturbations of the translational-rotational motion in the problem of the two non-stationary bodies: sphere - axisymmetric body. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 76, n. 1, p. 71-81, feb. 2015. ISSN 1563-0277. Available at: <http://bm.kaznu.kz/index.php/kaznu/article/view/89>. Date accessed: 23 may 2019.
Section
Mechanics, Mathematics, Computer Science

Keywords

variable mass; secular perturbation; axisymmetric body; variable oblate; translational- rotational motion;