The stability of the rotation of a magnetized gyro with a fixed point

Abstract

In conventional studies about the gyro motion the gyroscopic forces which are produced by the Lorentz action of the magnetic field on the electrical charges moving in space have not been considered. Euler gyro, Lagrange gyro and Kovalveskaya gyro are three representative gyros. In this paper, the stability and instability conditions of the rotation of the three representative gyros under the action of the Lorentz forces both in a uniform force field and in a central force field are obtained by using Liapunov's direct method.