10.26731/1813-9108.2017.3(55).17-22
The qualitative analysis for the equations of motion of a gyrostat in ideal fluid is conducted in the article. The motion of the gyrostat on the surface defined by the zeroth level of area integral is considered. The mass geometry of the body and the initial conditions of its motion correspond to the Chaplygin integrable case. For the equations of motion of the gyrostat, in the framework of their qualitative analysis, the families of stationary solutions have been found. In the original phase space, the elements of these families correspond to permanent helical and translational motions of the body. It is shown that the found solutions belong to invariant manifolds of codimension 2. Lyapunov sufficient stability conditions have been obtained for the stationary solutions. Stability, with respect to a part of the phase variables, has been derived for the stationary invariant manifolds.
Работа частично поддержана Советом по грантам Президента РФ для государственной поддержки ведущих научных школ РФ (НШ-8081.2016.9) и грантом РФФИ (грант 16-07-00201а).
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