According to the theorem of Lord Kelvin, an unstable conservative system can be stabilized by the gyroscopic force when the number of positive real characteristic roots is even without zero characteristic roots. In this paper, it is proved that an unstable conservative system with zero characteristic roots and an odd number of positive real characteristic roots can also be stabilized by the gyroscopic force. As an application of the theorem of Lord Kelvin, the stability problem in a noninertial reference frame rotating with constant angular velocity is also discussed. The rotating coordinates system is regarded as a formal conservative system with potential energy including the field of centrifugal inertial force. But the rotating system is not equivalent to the conservative inertial system, because there exists the Coriolis inertial force in perturbed motion. Therefore, the Lagrange theorem of minimal potential energy is not allowed to determine the stability in the formal conservative system. However, when the complimentary condition of Kelvin′s theorem is employed, the unstable formal conservative system can be stabilized by the Coriolis inertial force. The stability problems of twobody system with circle orbit and the Lagrange points of restrict threebody problem are analyzed as examples. Both systems under the action of gravitational and centrifugal force are unstable with one zero and one positive real characteristic root. When the Coriolis inertial force is considered, both unstable systems can be changed to be stable.