About Stationary Movements of the Generalized Kovalevskaya Top and Their Stability

Abstract

A qualitative analysis of the equations of motion of the Kovalevskaya top in a double constant field of forces is carried out. In the framework of this study, it was established that in the case of parallel force fields, the equations of motion of the body have families of permanent rotations, in the case of orthogonal ones they have pendulum-type movements, with special orientation of force fields they have families of equilibrium positions. It is shown that the solutions belong either to one of the two invariant manifolds of codimension 2, or to their intersection. For the solutions found, necessary and sufficient conditions of Lyapunov stability are obtained.