Symbolic–numeric investigations for stability analysis of Lagrange systems

An approach for symbolic–numeric stability analysis of equilibrium positions of a satellite system with given gyrostatic and aerodynamic torques and given principal central moments of inertia is presented. The satellite system is described by Lagrange differential equations. The equations of motion form a closed system, for which the Jacobi Integral is valid. It is shown that 24 isolated equilibrium positions exist when the modulus of the gyrostatic torque vector and the modulus of the aerodynamic torque vector are sufficiently small. The stability of the equilibrium positions are analyzed numerically.