In this paper a mnechanical system is studied in which a rotor rotates around a fixed axis with a string suspended symmetric rigid body.All relative equilibrium strates and their stability are discussed.Considering the spinning angular velocity ω around the fixed vertical axis as a parameter,algebraic equations with this parameter are obtained,Every solution of the equations is relevant to a relative equilibrium state of the system.The existence of two important relative equilibrium states is discussed by numerical method developed in bifurcation theory in this paper,In addition,The lagrange's Theorem is used to determine the stability of the relative equilibrium state relevant to the solution of the algebraic equations.
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