On deformable satellite plane motion in central gravitational field relative to the center of mass

Аuthors

Skorobogatykh I. V.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: igorsko@rambler.ru

Abstract

The problem of the satellite, consisting of axially symmetric solid and deformable parts, motion relative to the center of mass is studied in the case, when its center of mass is moving in a circular orbit around the center of gravitation attraction. The Voigt-Kelvin model is used for deformable material description. Equation of deformations and motion around the center of mass is obtained using d’Alembert-Lagrange variation principle. The elastic displacement vector is expanded in series of free oscillations nodes of deformed part of the satellite. These nodes are orthonormal. The deformations are considered as quasi-static. This is used for obtaining of approximate solution of deformation equations. These solutions are substituted in equations of rotation. The special case of plane rotations of satellite is considered. Two series of the satellite equilibrium positions in orbital coordinate system are found. The first is the case when the satellite symmetry axis is directed along the radius vector of the center of mass, and the second is the case when the satellite symmetry axis is orthogonal to the radius vector of the center of mass. The first series of equilibrium positions is asymptotically stable, and the second is unstable. The work shows that the evolution of every plane rotational motion tends to the first equilibrium position. Thus, it is shown that the satellite is captured in a stable equilibrium position, in which the satellite symmetry axis is directed along the radius vector of the center of mass in the orbital system coordinate.

Keywords:

attractive center, axisymmetric satellite, linear theory of viscoelasticity, the evolution of rotary motion

References

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