The spinning bodies motion stability by lyapunov in an axially symmetric gravitational field

The stability by Lyapunov of the circular motion of spinning test bodies in a Lense-Thirring field has been investigated. For Papapetrou's equations the generalized supplementary conditionsS ^oi U _o =kS ^ij U _j ,k=const.,i, j = 1, 2, 3 have been chosen. Four of the first integrals of motion have been indicated. The existence, stability, and instability regions have been found. It is shown that the positions of stability and instability ranges depend considerably upon the type of supplementary conditions.