Symbolic-numerical methods of studying equilibrium positions of a gyrostat satellite

Methods of computer algebra are used to study properties of a nonlinear algebraic system that determines equilibrium positions of a gyrostat satellite moving along a circular orbit. Bifurcation values of parameters such that the number of equilibrium positions changes are found numerically. Detailed numerical analyses of evolution of existence domains of different numbers of equilibria in the space of dimensionless parameters are performed.