THE STABILITY OF THE ROTATION OF STEKLOV GYRO

In both uniform gravitational field and Newtonian central gravitationa l Geld, the conditions of stability and instability of the permanent r otation of the Steklov gyro with linear damping or nonlinear damping t orques are studied by the Liapunov direct method and the first approxi mation method. Additionally, some new theorems are used in finding the stability and asymptotic stability of the gyro motion. In the Newtoni an central gravitational field for the sake of high accuracy, the seco nd order term of IIR in the expression of potential energy has been co nsidered, where R is the distance between the mass center of the gyro and the center of the earth. Numerical results are presented to show t he domains of attraction in two cases by using a cell-to-cell mapping, the effects of types of damping torque and the system parameters on t he gyro motion are also discussed in these cases.