Application of Computer Algebra Methods to Investigate the Dynamics of the System of Two Connected Bodies Moving along a Circular Orbit

Abstract

Computer algebra methods are used to investigate properties of a nonlinear algebraic system that determines the equilibrium orientations for a system of two bodies connected by a spherical hinge that moves along a circular orbit under the action of gravitational torque. To determine the equilibrium orientations for the system of two bodies, the system of 12 stationary algebraic equations is decomposed using linear algebra methods and algorithms for Gröbner basis construction. Depending on the parameters of the problem, the number of equilibria is found by analyzing the real roots of the algebraic equations from the Gröbner basis constructed. Evolution of the conditions for equilibria existence in the dimensionless parameter space of the problem is investigated. The effectiveness of the algorithms for Gröbner basis construction is analyzed depending on the number of parameters for the problem under consideration.