Symbolic Investigation of the Dynamics of a System of Two Connected Bodies Moving Along a Circular Orbit

Abstract

The dynamics of the system of two bodies, connected by a spherical hinge, that moves along a circular orbit under the action of gravitational torque is investigated. Computer algebra method based on the resultant approach was applied to reduce the satellite stationary motion system of algebraic equations to a single algebraic equation in one variable that determines all planar equilibrium configurations of the two–body system. Classification of domains with equal numbers of equilibrium solutions is carried out using algebraic methods for constructing discriminant hypersurfaces. Bifurcation curves in the space of system parameters that determine boundaries of domains with a fixed number of equilibria of the two–body system were obtained symbolically. Depending on the parameters of the problem, the number of equilibria was found by analyzing the real roots of the algebraic equations.