About the class of asymptotically precessional motions of a spherical gyrostat under the action of potential and gyroscopic forces (Q2880015)

This paper investigates movements in cases where the speed of rotation of the precession and speed are constant. The motion is described by the Kirchhoff-Poisson equations of the gyrostat. Conditions on the parameters that characterize the right-hand sides of these equations under which the motion is asymptotic to the regular precession. The equations of motion are constructed. The system of variational equations is reduced to the Hill equation. Sufficient conditions for the existence of motions of a gyrostat are obtained using the Lyapunov method. An algorithm for constructing Lyapunov series based on the method of successive approximations is given.