Stability of Euler, Lagrange and Kovalevskaya gyros in a Newtonian central force field with second order terms

Abstract

The stability of the permanent rotation of the Euler, Lagrange and Kovalevskaya gyros about a fixed point in the Newtonian central force field is investigated by Liapunov direct method, which improve Leimanis' and Rumiantsev's result of stability conditions. For the sake of high accuracy, the first and second order terms of R(-1) expressed by potential energy of the Newtonian central force field have been considered, where the R is the distance from the fixed point to the center of attraction.