On the orbital stability of a periodic solution of the equations of motion of a Kovalevskaya gyroscope
The sufficient conditions for the orbital stability of a periodic solution of the equations of motion of a Kovalevskaya gyroscope in the case of Bobylev-Steklov integrability are obtained. It is difficult to expect Lyapunov stability for the unsteady motions of a heavy solid having a fixed point since a dependence of the vibrations frequency on the initial conditions is characteristic for the simplest of them, i.e. periodic motions. Moreover, a rougher property of periodic solutions of the Euler-Poisson equations, orbital stability, is not the subject of special investigations in the dynamics of a solid. The algorithm of the present investigation utilizes the treatment ascribed Zhukovskii of orbital stability as the Lyapunov stability of motion for a special selection of the variable playing the part of time and the Chetayev method of constructing Lyapunov functions from the first integrals of the equations of perturbed motion. This latter circumstance enables the Chetayev method to be put in one series with the methods used earlier.
first integrals of the equations of perturbed motion
scientific article; zbMATH DE number 4022697
scientific article