SOME THEOREMS FOR DETERMINING THE DEFINITENESS AND CHANGEABILITY OF SIGN OF FUNCTIONS AND THE APPLICATION TO THE CONDITIONAL STABILITY OF THE MOTION OF THE AXIS OF A SLEEPING TOP

This paper gives some theorems for determiningthe definiteness and changeabilitg of sign of func-tions as well as the application to the axis of asleeping top.The necessarg and sufficient condi-tion of the conditional stabilitg of the rotion isobtained.Which coincides With that.of the stabilitgof nutation angle and also with that of the stabili-ty of total variables in the equations of cotion.