Studying the stability boundaries of the gyro-stabilized satellite on a circular orbit

Consideration was given to all parts of the stability boundaries of stationary motion of the gyro-stabilized manyaxis satellite. For each of the necessary stability conditions, conversion to zero or equality was analyzed using the second Lyapunov method. Terms of orders higher than two were used to check sign-definiteness of the Lyapunov function on the stability boundaries. Using the terms up to the sixth order, analysis established asymptotic stability on some parts of the boundaries. Terms of the order at most four enabled us to prove instability on other parts of the boundary.