On new solutions of the Kirchhoff equations in the case of asymptotically uniform motion of a spherical gyrostat. (Q2901606)

The motion equations of a spherical gyrostat under the action of potential and gyroscopic forces are considered in the paper. The dynamics is governed by three Kirchhoff's equations with respect to the angular velocity vector and three Poisson's equations with respect to the symmetry vector of the force field. A family of uniform rotations of the gyrostat is introduced depending on the angular velocity parameter. The author studies asymptotical motions for such a family of uniform rotations. The existence of an asymptotically uniform motion is established by using the Lyapunov series.