Dynamics of a System of Two Connected Bodies Moving along a Circular Orbit around the Earth

¹ MGIMO University, Prospekt Vernadskogo 76, 119454 Moscow, Russia
² Moscow Institute of Physics and Technology, Institutskiy per. 9, 141700 Dolgoprudny, Russia
³ Keldysh Institute of Applied Mathematics RAS, Miusskaya Square 4, 125047 Moscow, Russia

^★ e-mail: s.gutnik@inno.mgimo.ru
^★★ e-mail: vas31@rambler.ru

Published online: 20 January 2020

Abstract

Symbolic–numeric methods are used to investigate the dynamics of a system of two bodies connected by a spherical hinge. The system is assumed to move along a circular orbit under the action of gravitational torque. The equilibrium orientations of the two-body system are determined by the real roots of a system of 12 algebraic equations of the stationary motions. Attention is paid to the study of the conditions of existence of the equilibrium orientations of the system of two bodies refers to special cases when one of the principal axes of inertia of each of the two bodies coincides with either the normal of the orbital plane, the radius vector or the tangent to the orbit. Nine distinct solutions are found within an approach which uses the computer algebra method based on the algorithm for the construction of a Gröbner basis.